Andrew L. Krause
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View article: Chase-and-Run and Chirality in Nonlocal Models of Pattern Formation
Chase-and-Run and Chirality in Nonlocal Models of Pattern Formation Open
Chase-and-run dynamics, in which one population pursues another that flees from it, are found throughout nature, from predator-prey interactions in ecosystems to the collective motion of cells during development. Intriguingly, in many of t…
View article: Transient Instability and Patterns of Reactivity in Diffusive-Chemotaxis Soil Carbon Dynamics
Transient Instability and Patterns of Reactivity in Diffusive-Chemotaxis Soil Carbon Dynamics Open
We study pattern formation in a chemotaxis model of bacteria and soil carbon dynamics as an example system where transient dynamics can give rise to pattern formation outside of Turing unstable regimes. We use a detailed analysis of the re…
View article: Designing reaction-cross-diffusion systems with Turing and wave instabilities
Designing reaction-cross-diffusion systems with Turing and wave instabilities Open
General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns wit…
View article: Pattern Formation as a Resilience Mechanism in Cancer Immunotherapy
Pattern Formation as a Resilience Mechanism in Cancer Immunotherapy Open
View article: Integral Asymptotics, Coalescing Saddles, and Multiple-scales Analysis of a Generalised Swift-Hohenberg Equation
Integral Asymptotics, Coalescing Saddles, and Multiple-scales Analysis of a Generalised Swift-Hohenberg Equation Open
Integral asymptotics play an important role in the analysis of differential equations and in a variety of other settings. In this work, we apply an integral asymptotics approach to study spatially localized solutions of a heterogeneous gen…
View article: Pattern Localisation in Swift-Hohenberg via Slowly Varying Spatial Heterogeneity
Pattern Localisation in Swift-Hohenberg via Slowly Varying Spatial Heterogeneity Open
Theories of localised pattern formation are important to understand a broad range of natural patterns, but are less well-understood than more established mechanisms of domain-filling pattern formation. Here, we extend recent work on patter…
View article: Designing reaction-cross-diffusion systems with Turing and wave instabilities
Designing reaction-cross-diffusion systems with Turing and wave instabilities Open
General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns wit…
View article: Turing Instabilities are Not Enough to Ensure Pattern Formation
Turing Instabilities are Not Enough to Ensure Pattern Formation Open
View article: Turing Pattern Formation in Reaction-Cross-Diffusion Systems with a Bilayer Geometry
Turing Pattern Formation in Reaction-Cross-Diffusion Systems with a Bilayer Geometry Open
Conditions for self-organisation via Turing’s mechanism in biological systems represented by reaction-diffusion or reaction-cross-diffusion models have been extensively studied. Nonetheless, the impact of tissue stratification in such syst…
View article: Interdependent Total Factor Productivity in an Input-Output model
Interdependent Total Factor Productivity in an Input-Output model Open
Industries learn productivity improvements from their suppliers. The observed empirical importance of these interactions, often omitted by input-output models, mandates larger attention. This article embeds interdependent total factor prod…
View article: Patterning of nonlocal transport models in biology: The impact of spatial dimension
Patterning of nonlocal transport models in biology: The impact of spatial dimension Open
Throughout developmental biology and ecology, transport can be driven by nonlocal interactions. Examples include cells that migrate based on contact with pseudopodia extended from other cells, and animals that move based on their awareness…
View article: VisualPDE: Rapid Interactive Simulations of Partial Differential Equations
VisualPDE: Rapid Interactive Simulations of Partial Differential Equations Open
View article: Turing instabilities are not enough to ensure pattern formation
Turing instabilities are not enough to ensure pattern formation Open
Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing's reaction--diffusion theory, which connects cellular signalling and transpor…
View article: Bat teeth illuminate the diversification of mammalian tooth classes
Bat teeth illuminate the diversification of mammalian tooth classes Open
View article: VisualPDE: rapid interactive simulations of partial differential equations
VisualPDE: rapid interactive simulations of partial differential equations Open
Computing has revolutionised the study of complex nonlinear systems, both by allowing us to solve previously intractable models and through the ability to visualise solutions in different ways. Using ubiquitous computing infrastructure, we…
View article: Patterning of nonlocal transport models in biology: the impact of spatial dimension
Patterning of nonlocal transport models in biology: the impact of spatial dimension Open
Throughout developmental biology and ecology, transport can be driven by nonlocal interactions. Examples include cells that migrate based on contact with pseudopodia extended from other cells, and animals that move based on their vision of…
View article: Turing pattern formation in reaction-cross-diffusion systems with a bilayer geometry
Turing pattern formation in reaction-cross-diffusion systems with a bilayer geometry Open
Conditions for self-organisation via Turing’s mechanism in biological systems represented by reaction-diffusion or reaction-cross-diffusion models have been extensively studied. Nonetheless, the impact of tissue stratification in such syst…
View article: The developmental basis of fingerprint pattern formation and variation
The developmental basis of fingerprint pattern formation and variation Open
Fingerprints are complex and individually unique patterns in the skin. Established prenatally, the molecular and cellular mechanisms that guide fingerprint ridge formation and their intricate arrangements are unknown. Here we show that fin…
View article: Concentration-Dependent Domain Evolution in Reaction–Diffusion Systems
Concentration-Dependent Domain Evolution in Reaction–Diffusion Systems Open
View article: Spatial heterogeneity localizes Turing patterns in reaction-cross-diffusion systems
Spatial heterogeneity localizes Turing patterns in reaction-cross-diffusion systems Open
Motivated by bacterial chemotaxis and multi-species ecological interactions in heterogeneous environments, we study a general one-dimensional reaction-cross-diffusion system in the presence of spatial heterogeneity in both transport and re…
View article: Spatial Heterogeneity Localizes Turing Patterns in Reaction-Cross-Diffusion Systems
Spatial Heterogeneity Localizes Turing Patterns in Reaction-Cross-Diffusion Systems Open
Motivated by bacterial chemotaxis and multi-species ecological interactions in heterogeneous environments, we study a general one-dimensional reaction-cross-diffusion system in the presence of spatial heterogeneity in both transport and re…
View article: Concentration-Dependent Domain Evolution in Reaction-Diffusion Systems
Concentration-Dependent Domain Evolution in Reaction-Diffusion Systems Open
Pattern formation has been extensively studied in the context of evolving (time-dependent) domains in recent years, with domain growth implicated in ameliorating problems of pattern robustness and selection, in addition to more realistic m…
View article: Fixed and Distributed Gene Expression Time Delays in Reaction–Diffusion Systems
Fixed and Distributed Gene Expression Time Delays in Reaction–Diffusion Systems Open
View article: Turing and wave instabilities in hyperbolic reaction–diffusion systems: The role of second-order time derivatives and cross-diffusion terms on pattern formation
Turing and wave instabilities in hyperbolic reaction–diffusion systems: The role of second-order time derivatives and cross-diffusion terms on pattern formation Open
View article: Fixed and Distributed Gene Expression Time Delays in Reaction-Diffusion Systems
Fixed and Distributed Gene Expression Time Delays in Reaction-Diffusion Systems Open
Time delays, modelling the process of intracellular gene expression, have been shown to have important impacts on the dynamics of pattern formation in reaction-diffusion systems. In particular, past work has shown that such time delays can…
View article: Vaginal Swabs Are Non-inferior to Endocervical Swabs for Sexually Transmitted Infection testing in the Emergency Department
Vaginal Swabs Are Non-inferior to Endocervical Swabs for Sexually Transmitted Infection testing in the Emergency Department Open
Study Objective: Emergency department (ED) testing for sexually transmitted infections (STI) in women is typically performed with a pelvic examination and an endocervical swab. However, vaginal swabs are effective for STI testing and the p…
View article: Turing and wave instabilities in hyperbolic reaction-diffusion systems:\n The role of second-order time derivatives and cross-diffusion terms on\n pattern formation
Turing and wave instabilities in hyperbolic reaction-diffusion systems:\n The role of second-order time derivatives and cross-diffusion terms on\n pattern formation Open
Hyperbolic reaction-diffusion equations have recently attracted attention\nboth for their application to a variety of biological and chemical phenomena,\nand for their distinct features in terms of propagation speed and novel\ninstabilitie…
View article: Bat teeth illuminate the diversification of mammalian tooth classes
Bat teeth illuminate the diversification of mammalian tooth classes Open
Tooth classes are a mammalian innovation that has contributed to the evolutionary success of mammals. However, our understanding of how tooth classes have evolved and diversified remains limited. Here, we use the evolutionary radiation of …
View article: Introduction to ‘Recent progress and open frontiers in Turing’s theory of morphogenesis’
Introduction to ‘Recent progress and open frontiers in Turing’s theory of morphogenesis’ Open
Elucidating pattern forming processes is an important problem in the physical, chemical and biological sciences. Turing's contribution, after being initially neglected, eventually catalysed a huge amount of work from mathematicians, physic…