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We study large-scale structure formation in the presence of a quintessence component with zero speed of sound in the framework of Eulerian Perturbation Theory. Due to the absence of pressure gradients, quintessence and dark matter are…

Cosmology and Nongalactic Astrophysics · Physics 2015-03-17 Emiliano Sefusatti , Filippo Vernizzi

We explore the dynamics of artificial one- and two-dimensional Ising-like quantum antiferromagnets with different lattice geometries by using a Rydberg quantum simulator of up to 36 spins in which we dynamically tune the parameters of the…

Most models of biological pattern formation are simulated on continuous domains even though cells are discrete objects that provide internal boundaries to the diffusion of regulatory components. In our previous papers on simulating…

Quantitative Methods · Quantitative Biology 2013-09-26 Jannik Vollmer , Denis Menshykau , Dagmar Iber

This study investigates transient wave dynamics in Turing pattern formation, focusing on waves emerging from localised disturbances. While the traditional focus of diffusion-driven instability has primarily centred on stationary solutions,…

Pattern Formation and Solitons · Physics 2024-03-15 Václav Klika , Eamonn A. Gaffney , Philip K. Maini

We study the thermally assisted relaxation of a directed elastic line in a two dimensional quenched random potential by solving numerically the Edwards-Wilkinson equation and the Monte Carlo dynamics of a solid-on-solid lattice model. We…

Statistical Mechanics · Physics 2009-09-10 José Luis Iguain , Sebastian Bustingorry , Alejandro B. Kolton , Leticia F. Cugliandolo

Organogenesis is a tightly regulated process that has been studied experimentally for decades. Computational models can help to integrate available knowledge and to better understand the underlying regulatory logic. We are currently…

Tissues and Organs · Quantitative Biology 2012-02-03 Philipp Germann , Dzianis Menshykau , Simon Tanaka , Dagmar Iber

The dynamics of linear stochastic growth equations on growing substrates is studied. The substrate is assumed to grow in time following the power law $t^\gamma$, where the growth index $\gamma$ is an arbitrary positive number. Two different…

Statistical Mechanics · Physics 2015-05-13 Carlos Escudero

I consider how cell shape and environmental geometry affect the rate of nutrient capture and the consequent maximum growth rate of a cell, focusing on rod-like species like \textit{E.\ coli}. Simple modeling immediately implies that it is…

Biological Physics · Physics 2014-03-27 Jonathan Landy

Spatiotemporal patterns are common in biological systems. For electrically-coupled cells previous studies of pattern formation have mainly used external forcing as the main bifurcation parameter. The purpose of this paper is to show that…

Dynamical Systems · Mathematics 2021-11-02 H. O. Fatoyinbo , R. G. Brown , D. J. W. Simpson , B. van Brunt

A method is created to automatically increase the threshold projection parameter in three-field density-based topology optimization to achieve a near binary design. The parameter increase each iteration is based on an exponential growth…

Optimization and Control · Mathematics 2024-04-23 Peter Donald Dunning

We study the macroscopic evolution of the growing cluster in the exactly solvable corner growth model with independent exponentially distributed waiting times. The rates of the exponentials are given by an addivitely separable function of…

Probability · Mathematics 2021-03-08 Elnur Emrah , Christopher Janjigian , Timo Seppäläinen

We study the bifurcation of planar patterns and fast-moving pattern interfaces in an asymptotic long-wave model for the three-dimensional B\'enard-Marangoni problem, which is close to a Turing instability. We derive the model from the full…

Analysis of PDEs · Mathematics 2024-10-04 Bastian Hilder , Jonas Jansen

We show by numerical simulations that discretized versions of commonly studied continuum nonlinear growth equations (such as the Kardar-Parisi-Zhang equation and the Lai-Das Sarma equation) and related atomistic models of epitaxial growth…

Condensed Matter · Physics 2009-10-28 C. Dasgupta , J. M. Kim , M. Dutta , S. Das Sarma

A stochastic partial differential equation along the lines of the Kardar-Parisi-Zhang equation is introduced for the evolution of a growing interface in a radial geometry. Regular polygon solutions as well as radially symmetric solutions…

Statistical Mechanics · Physics 2015-06-25 M. T. Batchelor , B. I. Henry , S. D. Watt

In many growth processes particles are highly mobile in an active layer at the surface, but are relatively immobile once incorporated in the bulk. We study models in which atoms are allowed to interact, equilibrate, and order on the…

Soft Condensed Matter · Physics 2009-10-31 Mehran Kardar

Models of bacterial growth tend to be `irreversible', allowing for the number of bacteria in a colony to increase but not to decrease. By contrast, models of molecular self-assembly are usually `reversible', allowing for addition and…

Statistical Mechanics · Physics 2017-10-18 Katherine Klymko , Juan P. Garrahan , Stephen Whitelam

A model for morphoelastic growth, that is, growth influenced by elastic stress, driven by the absorption of nutrients is considered. The model features a multiplicative decomposition of the deformation gradient into an elastic contribution…

Analysis of PDEs · Mathematics 2026-05-05 Helmut Abels , Julian Blawid , Georg Dolzmann

Growth-fragmentation processes model systems of cells that grow continuously over time and then fragment into smaller pieces. Typically, on average, the number of cells in the system exhibits asynchronous exponential growth and, upon…

Probability · Mathematics 2023-06-08 Emma Horton , Alexander R. Watson

We study the high temperature phase of a family of typed branching diffusions initially studied in [Ast\'{e}risque 236 (1996) 133--154] and [Lecture Notes in Math. 1729 (2000) 239--256 Springer, Berlin]. The primary aim is to establish some…

Probability · Mathematics 2007-05-23 Y. Git , J. W. Harris , S. C. Harris

We introduce a model for describing the defected growth of striped patterns. This model, while roughly related to the Swift-Hohenberg model, generates a quite different mixture of defects during phase ordering. We find two characteristic…

Soft Condensed Matter · Physics 2009-11-10 Hai Qian , Gene F. Mazenko