To this day, computer models for stromatolite formation have made substantial use of the Kardar-Parisi-Zhang (KPZ) equation. Oddly enough, these studies yielded mutually exclusive conclusions about the biotic or abiotic origin of such structures. We show in this paper that, at our current state of knowledge, a purely biotic origin for stromatolites can neither be proved nor disproved by means of a KPZ-based model. What can be shown, however, is that whatever their (biotic or abiotic) origin might be, some morphologies found in actual stromatolite structures (e.g. overhangs) cannot be formed as a consequence of a process modelled exclusively in terms of the KPZ equation and acting over sufficiently large times. This suggests the need to search for alternative mathematical approaches to model these structures, some of which are discussed in this paper.
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http://dx.doi.org/10.1098/rsif.2011.0516 | DOI Listing |
Phys Rev E
November 2024
Université Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France.
A new scaling regime characterized by a z=1 dynamical critical exponent has been reported in several numerical simulations of the one-dimensional Kardar-Parisi-Zhang and noisy Burgers equations. In these works, this scaling, differing from the well-known KPZ one z=3/2, was found to emerge in the tensionless limit for the interface and in the inviscid limit for the fluid. Based on functional renormalization group, the origin of this scaling has been elucidated.
View Article and Find Full Text PDFPhys Rev E
June 2024
Université Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France.
We consider the one-dimensional deterministic complex Ginzburg-Landau equation in the regime of phase turbulence, where the order parameter displays a defect-free chaotic phase dynamics, which maps to the Kuramoto-Sivashinsky equation, characterized by negative viscosity and a modulational instability at linear level. In this regime, the dynamical behavior of the large wavelength modes is captured by the Kardar-Parisi-Zhang (KPZ) universality class, determining their universal scaling and their statistical properties. These modes exhibit the characteristic KPZ superdiffusive scaling with the dynamical critical exponent z=3/2.
View Article and Find Full Text PDFPhys Rev E
June 2024
Theory Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Calcutta 700064, West Bengal, India.
We elucidate the universal spatiotemporal scaling properties of the time-dependent correlation functions in a class of two-component one-dimensional (1D) driven diffusive system that consists of two coupled asymmetric exclusion processes. By using a perturbative renormalization group framework, we show that the relevant scaling exponents have values same as those for the 1D Kardar-Parisi-Zhang (KPZ) equation. We connect these universal scaling exponents with the symmetries of the model equations.
View Article and Find Full Text PDFPhys Rev Lett
May 2024
Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium.
We show that lasing in flat-band lattices can be stabilized by means of the geometrical properties of the Bloch states, in settings where the single-particle dispersion is flat in both its real and imaginary parts. We illustrate a general projection method and compute the collective excitations, which display a diffusive behavior ruled by quantum geometry through a peculiar coefficient involving gain, losses and interactions, and entailing resilience against modulational instabilities. Then, we derive an equation of motion for the phase dynamics and identify a Kardar-Parisi-Zhang term of geometric origin.
View Article and Find Full Text PDFPhys Rev E
April 2024
Institut de Radioprotection et de Sûreté Nucléaire (IRSN) PSN-RES/SNC/LN, F-92260, Fontenay-aux-Roses, France.
An operating nuclear reactor is designed to maintain a sustained fission chain reaction in its core, which results from a delicate balance between neutron creations (i.e., fissions) and total absorptions.
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