Review
Engineering, Mechanical
Gui-Quan Sun, Hong-Tao Zhang, Jin-Shan Wang, Jing Li, Yi Wang, Li Li, Yong-Ping Wu, Guo-Lin Feng, Zhen Jin
Summary: This research delves into the key issue of population distribution in ecological systems and how it characterizes the relationship between populations, space-time structure, and evolution laws. It systematically summarizes the related results in pattern formation of ecological systems, showcasing the mechanisms of different patterns. This work offers valuable insights into understanding the complexity of ecosystems and can be applied in various related fields such as epidemiology, medical science, and atmospheric science.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Applied
Benjamin Aymard
Summary: This article introduces a unified framework to study reaction-diffusion systems with self- and cross-diffusion using a free energy approach. The framework leads to the formulation of an energy law and a numerical method. It provides an alternative method for studying nonlinear patterns and monitoring energy evolution in complex geometries.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics, Interdisciplinary Applications
Natham Aguirre, Michal Kowalczyk
Summary: This study investigates the problem of pattern formation using a one dimensional stochastic reaction-diffusion equation with time periodic coefficients. Large Deviations methods are applied to obtain lower bounds on the probability of developing certain evenly spaced patterns. The results suggest a correlation between the optimized number of interfaces and the length-scale parameter. Numerical simulations support the idea that the number of interfaces follows a certain law, even among unevenly spaced patterns.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Maria Vasilyeva, Alexey Sadovski, D. Palaniappan
Summary: This study considers a coupled nonlinear system of reaction-diffusion equations that describes the interactions of multiple components (species) with heterogeneous coefficients. A finite volume method is used to approximate the spatial domain and construct a semi-discrete form for numerical solutions. Two time approximation techniques, namely a fully implicit scheme and a semi-implicit scheme, are examined. To address the computational expense of the fully implicit scheme, an efficient and fast multiscale solver is proposed. This solver is based on an uncoupled system for each individual component and utilizes the Generalized Multiscale Finite Element Method (GMsFEM) to construct multiscale basis functions.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Engineering, Mechanical
Linhe Zhu, Le He
Summary: This paper analyzes the diffusion behavior of the suspicious and infected cabins in cyberspace using a rumor propagation reaction-diffusion model. The effects of time delay and changing diffusion coefficient are considered to study the stability and instability of the system. The existence of Hopf bifurcation induced by time delay is proven, and the necessary conditions for Turing instability are studied. Numerical simulations show that variations in diffusion coefficient and time delay can change the pattern type and affect the arrangement of crowd gathering areas.
NONLINEAR DYNAMICS
(2022)
Article
Multidisciplinary Sciences
Laszlo Mihaly Grob, Istvan Lagzi, Istvan Szalai
Summary: The mechanism proposed by Turing for reaction-diffusion systems is widely used to explain pattern formation in various fields. The persistence of patterns in changing environments is crucial in many natural cases. Experimental studies of these phenomena can be carried out using specially designed chemical systems, such as two-side-fed open gel reactors. By testing the effect of time-periodic boundary conditions on the dynamics of Turing patterns, this configuration allows for a better understanding of pattern formation in altering environments. Numerical simulations based on realistic chemistry and a 2D reactor description can reproduce feeding from boundaries and concentration gradients, revealing two regimes, spatiotemporal oscillations and pulsating spot patterns, with the possibility of a mixed-mode pattern. The findings suggest that periodic feeding can effectively control pattern formation in chemical systems.
ADVANCED THEORY AND SIMULATIONS
(2023)
Article
Mathematical & Computational Biology
Nazanin Zaker, Christina A. Cobbold, Frithjof Lutscher
Summary: This study explores the impact of landscape heterogeneity on the formation of Turing patterns in predator-prey interactions. By formulating reaction-diffusion equations on a patchy landscape and applying homogenization theory and stability analysis, we found mechanisms by which diffusion-driven instabilities may arise even if the local interaction and movement rates do not indicate it.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2022)
Article
Mathematics, Applied
Bartosz J. Bartmanski, Ruth E. Baker
Summary: The study explores the impact of various discretisations and methods for derivation of the diffusive jump rates on the outputs of stochastic simulations of reaction-diffusion models. It shows that while minor differences are observed for simple systems, significant variations can occur in model predictions for complex systems like Turing's diffusion-driven instability model of pattern formation. Care must be taken when using the reaction-diffusion master equation framework to make predictions for stochastic reaction-diffusion systems.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Physics, Multidisciplinary
Fridtjof Brauns, Henrik Weyer, Jacob Halatek, Junghoon Yoon, Erwin Frey
Summary: The study explores how wavelength selection in reaction-diffusion systems is achieved through a combination of coarsening processes and counteracting processes. By deriving a general coarsening criterion, it is found that coarsening is typically uninterrupted in systems that conserve mass.
PHYSICAL REVIEW LETTERS
(2021)
Article
Materials Science, Multidisciplinary
C. McNamara, J. M. Rickman, H. M. Chan
Summary: The study investigates the microstructural evolution that initiates from a compositionally inhomogeneous patterned structure in solid-state reactions and uses reaction-diffusion formalism to model the process. By connecting the spatio-temporal evolution of the product phase with the geometry and chemistry of the starting duplex structure, a better understanding of reaction kinetics and product microstructures is obtained. The results can be used to select templates judiciously to promote the formation of desirable microstructures and quantify important experimental kinetic parameters.
Article
Mathematics, Applied
Chengxia Lei, Guanghui Zhang, Jialin Zhou
Summary: In this paper, a biomass-water reaction-diffusion model with homogeneous Neumann boundary condition is studied to determine the conditions for the existence or non-existence of non-constant stationary solutions, providing criteria for the possibility of Turing patterns in the system. The results confirm previous numerical findings and complement theoretical results for the corresponding ODE model.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics, Applied
Alexander Kolinichenko, Lev Ryashko
Summary: This paper investigates a spatially extended stochastic reaction-diffusion model, demonstrating a theoretical approach and comparing statistically obtained data on stochastic sensitivity functions for stable nonhomogeneous stationary patterns. It discusses variations in pattern sensitivity to noise and the phenomenon of stochastic preference in different patterns in the Brusselator.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Alan R. Champneys, Fahad Al Saadi, Victor F. Brena-Medina, Veronica A. Grieneisen, Athanasius F. M. Maree, Nicolas Verschueren, Bert Wuyts
Summary: This paper presents a synthesis of recent research on the formation of localized patterns, isolated spots, or sharp fronts in models of natural processes governed by reaction-diffusion equations. It contrasts with the well-known Turing mechanism of periodic pattern formation and provides a general picture in one spatial dimension for models on long domains exhibiting sub-critical Turing instabilities.
PHYSICA D-NONLINEAR PHENOMENA
(2021)
Article
Mathematics, Interdisciplinary Applications
Priya Chakraborty, Mohit Kumar Jolly, Ushasi Roy, Sayantari Ghosh
Summary: Biological systems rely on bistability to exhibit non-genetic heterogeneity in cellular morphology and physiology. The spatial distribution of phenotypically heterogeneous cells, resulting from bistability, plays a significant role in phenomena such as biofilm development, adaptation, and cell motility. This paper investigates the pattern formation of a motif with non-cooperative positive feedback, which imposes a metabolic burden on its host. In-silico spatio-temporal diffusion is studied in cellular arrays in one and two dimensions with various initial conditions, and the stability of related states and the evolution of patterns are analyzed based on the variation of diffusion coefficients.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Physics, Multidisciplinary
Eric Cereceda-Lopez, Dominik Lips, Antonio Ortiz-Ambriz, Artem Ryabov, Philipp Maass, Pietro Tierno
Summary: The study demonstrates that hydrodynamic interactions between fluid-dispersed particles hinder transport across barriers in a flow-driven system, contrary to force-driven motion. This impact is shown to be a generic feature of flow-driven transport through a combination of experiments and theoretical models.
PHYSICAL REVIEW LETTERS
(2021)
Article
Chemistry, Physical
Alfredo Sciortino, Lukas J. Neumann, Timo Krueger, Ivan Maryshev, Tetsuhiko F. Teshima, Bernhard Wolfrum, Erwin Frey, Andreas R. Bausch
Summary: This study demonstrates the use of passive nematic materials to control the pattern formation process of active fluids by introducing and controlling defects. It shows that defects in the passive material can guide the flow of active microtubules and lead to the formation of macroscopic polar patterns, opening up new possibilities for shaping active materials using passive defects.
Article
Physics, Multidisciplinary
Moritz Striebel, Fridtjof Brauns, Erwin Frey
Summary: This study investigates the formation mechanism of cytoskeletal networks and finds that resource-limited length regulation can drive filament clustering and result in collective filament orientation in the clusters.
PHYSICAL REVIEW LETTERS
(2022)
Article
Multidisciplinary Sciences
Alexander Ziepke, Ivan Maryshev, Igor S. Aranson, Erwin Frey
Summary: This study demonstrates the crucial role of communication through chemical signals in the formation of complex structures among interacting agents at multiple scales. These findings provide insights into the self-organization in biological systems and offer potential applications in chemically driven colloids or microrobots.
NATURE COMMUNICATIONS
(2022)
Article
Multidisciplinary Sciences
Sabrina Meindlhumer, Fridtjof Brauns, Jernej Rudi Finzgar, Jacob Kerssemakers, Cees Dekker, Erwin Frey
Summary: Meindlhumer et al. have conducted a combined theoretical and experimental study on how the propagation direction of Min protein patterns can be changed by a bulk flow of solution. They demonstrate that the direction of in vitro Min protein patterns can be controlled by hydrodynamic flow, with downstream propagation for low concentration ratios of MinE:MinD, upstream propagation for large ratios, and multistability in between. Their study reveals the potential of using flow to probe molecular features and constrain mathematical models for pattern formation systems.
NATURE COMMUNICATIONS
(2023)
Article
Multidisciplinary Sciences
Iain F. Davidson, Roman Barth, Maciej Zaczek, Jaco van der Torre, Wen Tang, Kota Nagasaka, Richard Janissen, Jacob Kerssemakers, Gordana Wutz, Cees Dekker, Jan-Michael Peters
Summary: CTCF is a DNA-binding protein that establishes topologically associating domains (TADs) by blocking the diffusion and loop extrusion of cohesin. CTCF functions asymmetrically and is dependent on DNA tension. Moreover, CTCF regulates cohesin's loop-extrusion activity by changing its direction and inducing loop shrinkage. These results reveal mechanistic principles of how CTCF controls loop extrusion and genome architecture.
Article
Physics, Multidisciplinary
Meifang Fu, Tom Burkart, Ivan Maryshev, Henri G. Franquelim, Adrian Merino-Salomon, Maria Reverte-Lopez, Erwin Frey, Petra Schwille
Summary: Through a mechanochemical feedback loop involving Min proteins of Escherichia coli, liposomes start to move, which may help to design motile artificial cells.
Article
Physics, Multidisciplinary
Leonardo Demarchi, Andriy Goychuk, Ivan Maryshev, Erwin Frey
Summary: Enzyme-enriched condensates can regulate the distribution of their substrates and induce enzyme fluxes through feedback interactions. Weak feedback leads to condensate movement towards the center of a confined domain, while above a threshold, self-propulsion and oscillatory dynamics occur. Enzyme-driven fluxes can also result in interrupted coarsening and condensate division, leading to equidistant positioning.
PHYSICAL REVIEW LETTERS
(2023)
Article
Multidisciplinary Sciences
Zihang Wang, M. Cristina Marchetti, Fridtjof Brauns
Summary: Orientational order, encoded in anisotropic fields, is important in organism development. The study focuses on the freshwater polyp Hydra and its muscle fiber orientation defects. A minimal model is introduced to study the interaction between muscle fiber orientation, morphogen gradients, and body shape. The model successfully reproduces experimentally observed reorganization of orientational order on curved surfaces mimicking Hydra's morphologies.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2023)
Article
Physics, Fluids & Plasmas
Laeschkir Wuerthner, Andriy Goychuk, Erwin Frey
Summary: Intracellular protein patterns play a crucial role in regulating important cellular processes and their dynamics are influenced by changes in cell shape. To understand the underlying mechanisms, a conceptual model for cell polarity on a dynamic one-dimensional manifold is explored. The dynamics of the membrane shape induce pattern-forming instabilities and can also suppress pattern formation and shift existing patterns.
Article
Chemistry, Physical
Timo Krueger, Ivan Maryshev, Erwin Frey
Summary: Topological defects play a central role in the formation and organization of various biological systems. In this paper, agent-based simulations are used to study phase-separated active nematics and the formation of -1/2 defects. The authors investigate the morphology and characteristics of these defects, as well as observe and characterize lateral arc-like structures separating from nematic bands. The study also introduces a hydrodynamic theory that explains the emergence of defects and arcs.
Article
Physics, Fluids & Plasmas
Tom Burkart, Jan Willeke, Erwin Frey
Summary: This article investigates how periodic temporal environmental variation can affect the composition and biodiversity of an ecosystem. By using a population dynamics model and timescale separation, the study shows that the impact of environmental changes on species coexistence and stability depends on the timescale of the changes.
Review
Physics, Applied
Tom Burkart, Manon C. Wigbers, Laeschkir Wurthner, Erwin Frey
Summary: Proteins play a crucial role in controlling various vital functions in living cells. Understanding the formation of protein patterns inside cells is essential for comprehending information processing in biological systems.
NATURE REVIEWS PHYSICS
(2022)