61 citations · 144 across the 18 of their papers we have counts for
21 papers
Patterns in Time and Space from a Single Morphogen via Nonlinear Layering
N. Mahashri, Andrew L. Krause, M. Chandru +1
Spatial and temporal pattern formation in reaction-diffusion systems is typically studied with two or more equations, as scalar reaction-diffusion equations confined to convex doma…
Turing instabilities are not enough to ensure pattern formation
Andrew L. Krause, Eamonn A. Gaffney, Thomas Jun Jewell +2
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--diffus…
VisualPDE: rapid interactive simulations of partial differential equations
Benjamin J. Walker, Adam K. Townsend, Alexander K. Chudasama +1
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 di…
Patterning of nonlocal transport models in biology: the impact of spatial dimension
Thomas Jun Jewell, Andrew L. Krause, Philip K. Maini +1
Throughout developmental biology and ecology, transport can be driven by nonlocal interactions. Examples include cells that migrate based on contact with pseudopodia extended from…
Spatial Heterogeneity Localizes Turing Patterns in Reaction-Cross-Diffusion Systems
Eamonn A. Gaffney, Andrew L. Krause, Philip K. Maini +1
Motivated by bacterial chemotaxis and multi-species ecological interactions in heterogeneous environments, we study a general one-dimensional reaction-cross-diffusion system in the…
Concentration-Dependent Domain Evolution in Reaction-Diffusion Systems
Andrew L. Krause, Eamonn A. Gaffney, Benjamin J. Walker
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 patter…
Fixed and Distributed Gene Expression Time Delays in Reaction-Diffusion Systems
Alec Sargood, Eamonn A. Gaffney, Andrew L. Krause
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. I…
Turing and wave instabilities in hyperbolic reaction-diffusion systems: The role of second-order time derivatives and cross-diffusion terms on pattern formation
Joshua Ritchie, Andrew L. Krause, Robert A. Van Gorder
Hyperbolic reaction-diffusion equations have recently attracted attention both for their application to a variety of biological and chemical phenomena, and for their distinct featu…
Modern Perspectives on Near-Equilibrium Analysis of Turing Systems
Andrew L. Krause, Eamonn A. Gaffney, Philip K. Maini +1
In the nearly seven decades since the publication of Alan Turing's work on morphogenesis, enormous progress has been made in understanding both the mathematical and biological aspe…
Isolating Patterns in Open Reaction-Diffusion Systems
Andrew L. Krause, Václav Klika, Philip K. Maini +2
Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. Howev…
Turing Patterning in Stratified Domains
Andrew L. Krause, Václav Klika, Jacob Halatek +4
Reaction-diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal-mesenchymal coupling in developm…
Unstaggered-staggered solitons on one- and two-dimensional two-component discrete nonlinear Schrödinger lattices
Robert A. Van Gorder, Andrew L. Krause, Boris A. Malomed +1
We study coupled unstaggered-staggered soliton pairs emergent from a system of two coupled discrete nonlinear Schrödinger (DNLS) equations with the self-attractive on-site self-pha…
From One Pattern into Another: Analysis of Turing Patterns in Heterogeneous Domains via WKBJ
Andrew L. Krause, Václav Klika, Thomas E. Woolley +1
Pattern formation from homogeneity is well-studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is nontrivial to separate observed spati…
Turing conditions for pattern forming systems on evolving manifolds
Robert A. Van Gorder, Václav Klika, Andrew L. Krause
The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in d…
Amplitude death criteria for coupled complex Ginzburg-Landau systems
Robert A. Van Gorder, Andrew L. Krause, James A. Kwiecinski
Amplitude death, which occurs in a system when one or more macroscopic wavefunctions collapse to zero, has been observed in mutually coupled solid-state lasers, analog circuits, an…
Chaotic dynamics in the planar gravitational many-body problem with rigid body rotations
James A. Kwiecinski, Attila Kovacs, Andrew L. Krause +2
The discovery of Pluto's small moons in the last decade brought attention to the dynamics of the dwarf planet's satellites. With such systems in mind, we study a planar -body sy…
Coupled complex Ginzburg-Landau systems with saturable nonlinearity and asymmetric cross-phase modulation
Robert A. Van Gorder, Andrew L. Krause, Ferran Brosa Planella +1
We formulate and study dynamics from a complex Ginzburg-Landau system with saturable nonlinearity, including asymmetric cross-phase modulation (XPM) parameters. Such equations can…
Bifurcations and dynamics emergent from lattice and continuum models of bioactive porous media
Andrew L. Krause, Dmitry Beliaev, Robert A. Van Gorder +1
We study dynamics emergent from a two-dimensional reaction--diffusion process modelled via a finite lattice dynamical system, as well as an analogous PDE system, involving spatiall…
Lattice and Continuum Modelling of a Bioactive Porous Tissue Scaffold
Andrew L. Krause, Dmitry Beliaev, Robert A. Van Gorder +1
A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of n…
Asymptotic Dynamics of Stochastic -Laplace Equations on Unbounded Domains
Andrew Krause
This thesis is concerned with the asymptotic behavior of solutions of stochastic -Laplace equations driven by non-autonomous forcing on . Two cases are studied, wi…
Pullback Attractors of Non-autonomous Stochastic Degenerate Parabolic Equations on Unbounded Domains
Andrew Krause, Bixiang Wang
This paper is concerned with pullback attractors of the stochastic p-Laplace equation defined on the entire space R^n. We first establish the asymptotic compactness of the equation…