New dynamic scaling in increasing systems

Pastor, M.; Galeano, Javier

doi:10.2478/s11534-007-0043-4

Cited by 13 publications

(17 citation statements)

References 13 publications

(19 reference statements)

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“…Scaling exponents for interface growth models on expanding domains were recently analyzed [10,28,29]. Since the spatial correlation length increases as ξ ∼ ∥ t z 1 , where z is the dynamic exponent, for a substrate increasing as ∼ γ L t , the interface width evolves indefinitely as ∼ β W t if γ = > z 1 1 , because correlation length never reaches the system size [28]. Otherwise, for γ < z 1 the surface becomes completely correlated ξ ∼ L ( ) after a crossover time and the interface width scales as ∼ γα W t [28], where α β = z is the roughness exponent.…”

Section: Introductionmentioning

confidence: 99%

Interface fluctuations for deposition on enlarging flat substrates

2014

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We investigate solid-on-solid models that belong to the Kardar-Parisi-Zhang (KPZ) universality class on substrates that expand laterally at a constant rate by duplication of columns. Despite the null global curvature, we show that all investigated models have asymptotic height distributions and spatial covariances in agreement with those expected for the KPZ subclass for curved surfaces. In 1 + 1 dimensions, the height distribution and covariance are given by the GUE Tracy-Widom distribution and the Airy 2 process instead of the GOE and Airy 1 foreseen for flat interfaces. These results imply that when the KPZ class splits into curved and flat subclasses, as conventionally considered, the expanding substrate may play a role equivalent to, or perhaps more important than, the global curvature. Moreover, the translational invariance of the interfaces evolving on growing domains allowed us to accurately determine, in 2 + 1 dimensions, the analog of the GUE Tracy-Widom distribution for height distribution and that of the Airy 2 process for spatial covariance. Temporal covariance is also calculated and shown to be universal in each dimension and in each of the two subclasses. A logarithmic correction associated with the duplication of columns is observed and theoretically elucidated. Finally, crossover between regimes with fixed-size and enlarging substrates is also investigated.

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Section: Introductionmentioning

confidence: 99%

Interface fluctuations for deposition on enlarging flat substrates

2014

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“…The scaling analysis of tumor growth fronts, as well as those from different cell line colony 2D profiles, has been used to determine the universality class involved in their growth processes [5], and scaling data were interpreted by the molecular beam epitaxy (MBE) model. This conclusion was revisited to assure whether the validity of extending the mathematical formalism for fixed size colony growth experiments was directly applicable to radially expanding systems [14][15][16]. However, in contrast with the MBE model, scaling exponents derived from a cellular automaton model for 2D colony growth dynamics appeared to be much likely to be represented by the Kardar, Parisi, and Zhang (KPZ) -type continuous equation [17].…”

Section: Introductionmentioning

confidence: 99%

Growth dynamics of cancer cell colonies and their comparison with noncancerous cells

et al. 2012

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The two-dimensional (2D) growth dynamics of HeLa (cervix cancer) cell colonies was studied following both their growth front and the pattern morphology evolutions utilizing large population colonies exhibiting linearly and radially spreading fronts. In both cases, the colony profile fractal dimension was d f = 1.20 ± 0.05 and the growth fronts displaced at the constant velocity 0.90 ± 0.05 μm min −1 . Colonies showed changes in both cell morphology and average size. As time increased, the formation of large cells at the colony front was observed. Accordingly, the heterogeneity of the colony increased and local driving forces that set in began to influence the dynamics of the colony front. The dynamic scaling analysis of rough colony fronts resulted in a roughness exponent α = 0.50 ± 0.05, a growth exponent β = 0.32 ± 0.04, and a dynamic exponent z = 1.5 ± 0.2. The validity of this set of scaling exponents extended from a lower cutoff l c ≈ 60 μm upward, and the exponents agreed with those predicted by the standard Kardar-Parisi-Zhang continuous equation. HeLa data were compared with those previously reported for Vero cell colonies. The value of d f and the Kardar-Parisi-Zhang-type 2D front growth dynamics were similar for colonies of both cell lines. This indicates that the cell colony growth dynamics is independent of the genetic background and the tumorigenic nature of the cells. However, one can distinguish some differences between both cell lines during the growth of colonies that may result from specific cooperative effects and the nature of each biosystem.

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“…However, in the inflating geometry investigated in the present work, the interface width does not saturate and this definition loses meaning. See also discussions in Refs [15,21]…”

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confidence: 97%

“…Particular interest is given to the rough interfaces of compact and spherical patterns observed in bacterial colonies [4][5][6][7][8] and clusters of normal [9][10][11] and tumor [12,13] cells grown on culture under controlled experimental conditions. The Eden model [14] is a benchmark of stochastic processes, in the important class of growth models on expanding substrates [15][16][17][18][19][20][21], which forms radial clusters with irregular (fractal) borders. In this model, new cells are irreversibly added at random positions of the neighborhood of previously existent cells.…”

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confidence: 99%

Eden model with nonlocal growth rules and kinetic roughening in biological systems

Santalla

Ferreira

2018

Phys. Rev. E

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We investigate an off-lattice Eden model where the growth of new cells is performed with a probability dependent on the availability of resources coming externally towards the growing aggregate. The concentration of nutrients necessary for replication is assumed to be proportional to the voids connecting the replicating cells to the outer region, introducing therefore a nonlocal dependence on the replication rule. Our simulations point out that the Kadar-Parisi-Zhang (KPZ) universality class is a transient that can last for long periods in plentiful environments. For conditions of nutrient scarcity, we observe a crossover from regular KPZ to unstable growth, passing by a transient consistent with the quenched KPZ class at the pinning transition. Our analysis sheds light on results reporting on the universality class of kinetic roughening in akin experiments of biological growth.

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New dynamic scaling in increasing systems

Cited by 13 publications

References 13 publications

Interface fluctuations for deposition on enlarging flat substrates

Interface fluctuations for deposition on enlarging flat substrates

Growth dynamics of cancer cell colonies and their comparison with noncancerous cells

Eden model with nonlocal growth rules and kinetic roughening in biological systems

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