Search Results - "Krause, Andrew L"

Turing–Hopf patterns on growing domains: The torus and the sphere by Sánchez-Garduño, Faustino, Krause, Andrew L., Castillo, Jorge A., Padilla, Pablo

“…•Turing and Turing–Hopf bifurcations induce spatio-temporal patterns on manifolds.•Growth and curvature modulate pattern selection and determine qualitative…”
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Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds by Krause, Andrew L., Ellis, Meredith A., Van Gorder, Robert A.

“…We study two-species reaction–diffusion systems on growing manifolds, including situations where the growth is anisotropic yet dilational in nature. In…”
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Introduction to 'Recent progress and open frontiers in Turing's theory of morphogenesis' by Krause, Andrew L, Gaffney, Eamonn A, Maini, Philip K, Klika, Václav

“…Elucidating pattern forming processes is an important problem in the physical, chemical and biological sciences. Turing's contribution, after being initially…”
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Bat teeth illuminate the diversification of mammalian tooth classes by Sadier, Alexa, Anthwal, Neal, Krause, Andrew L., Dessalles, Renaud, Lake, Michael, Bentolila, Laurent A., Haase, Robert, Nieves, Natalie A., Santana, Sharlene E., Sears, Karen E.

“…Tooth classes are an innovation that has contributed to the evolutionary success of mammals. However, our understanding of the mechanisms by which tooth…”
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Modern perspectives on near-equilibrium analysis of Turing systems by Krause, Andrew L, Gaffney, Eamonn A, Maini, Philip K, Klika, Václav

“…In the nearly seven decades since the publication of Alan Turing's work on morphogenesis, enormous progress has been made in understanding both the…”
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Bespoke Turing Systems by Woolley, Thomas E., Krause, Andrew L., Gaffney, Eamonn A.

“…Reaction–diffusion systems are an intensively studied form of partial differential equation, frequently used to produce spatially heterogeneous patterned…”
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From one pattern into another: analysis of Turing patterns in heterogeneous domains via WKBJ by Krause, Andrew L, Klika, Václav, Woolley, Thomas E, Gaffney, Eamonn A

“…Pattern formation from homogeneity is well studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is non-trivial to…”
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Turing conditions for pattern forming systems on evolving manifolds by Van Gorder, Robert A., Klika, Václav, Krause, Andrew L.

“…The study of pattern-forming instabilities in reaction–diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings,…”
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Fixed and Distributed Gene Expression Time Delays in Reaction–Diffusion Systems by Sargood, Alec, Gaffney, Eamonn A., Krause, Andrew L.

“…Time delays, modelling the process of intracellular gene expression, have been shown to have important impacts on the dynamics of pattern formation in…”
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Stochastic epidemic metapopulation models on networks: SIS dynamics and control strategies by Krause, Andrew L., Kurowski, Lawrence, Yawar, Kamran, Van Gorder, Robert A.

“…•A stochastic metapopulation SIS epidemic model is proposed on spatial networks.•For large time solutions tend to quasi-stationary distributions in the…”
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Generalist predator dynamics under kolmogorov versus non-Kolmogorov models by Xu, Yifang, Krause, Andrew L., Van Gorder, Robert A.

“…Ecosystems often contain multiple species across two or more trophic levels, with a variety of interactions possible. In this paper we study two classes of…”
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Patterning of nonlocal transport models in biology: The impact of spatial dimension by Jewell, Thomas Jun, Krause, Andrew L., Maini, Philip K., Gaffney, Eamonn A.

“…Throughout developmental biology and ecology, transport can be driven by nonlocal interactions. Examples include cells that migrate based on contact with…”
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Beyond Onsager–Casimir Relations: Shared Dependence of Phenomenological Coefficients on State Variables by Klika, Václav, Krause, Andrew L

“…Phenomenological coefficients in linear nonequilibrium thermodynamics have been considered to be independent, apart from restrictions due to the…”
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The developmental basis of fingerprint pattern formation and variation by Glover, James D., Sudderick, Zoe R., Shih, Barbara Bo-Ju, Batho-Samblas, Cameron, Charlton, Laura, Krause, Andrew L., Anderson, Calum, Riddell, Jon, Balic, Adam, Li, Jinxi, Klika, Václav, Woolley, Thomas E., Gaffney, Eamonn A., Corsinotti, Andrea, Anderson, Richard A., Johnston, Luke J., Brown, Sara J., Wang, Sijia, Chen, Yuhang, Crichton, Michael L., Headon, Denis J.

“…Fingerprints are complex and individually unique patterns in the skin. Established prenatally, the molecular and cellular mechanisms that guide fingerprint…”
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Concentration-Dependent Domain Evolution in Reaction–Diffusion Systems by Krause, Andrew L., Gaffney, Eamonn A., Walker, Benjamin J.

“…Pattern formation has been extensively studied in the context of evolving (time-dependent) domains in recent years, with domain growth implicated in…”
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A Non-local Cross-Diffusion Model of Population Dynamics II: Exact, Approximate, and Numerical Traveling Waves in Single- and Multi-species Populations by Krause, Andrew L., Van Gorder, Robert A.

“…We study traveling waves in a non-local cross-diffusion-type model, where organisms move along gradients in population densities. Such models are valuable for…”
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Isolating Patterns in Open Reaction–Diffusion Systems by Krause, Andrew L., Klika, Václav, Maini, Philip K., Headon, Denis, Gaffney, Eamonn A.

“…Realistic examples of reaction–diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or…”
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VisualPDE: Rapid Interactive Simulations of Partial Differential Equations by Walker, Benjamin J., Townsend, Adam K., Chudasama, Alexander K., Krause, Andrew L.

“…Computing has revolutionised the study of complex nonlinear systems, both by allowing us to solve previously intractable models and through the ability to…”
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Turing Instabilities are Not Enough to Ensure Pattern Formation by Krause, Andrew L., Gaffney, Eamonn A., Jewell, Thomas Jun, Klika, Václav, Walker, Benjamin J.

“…Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in…”
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A Non-local Cross-Diffusion Model of Population Dynamics I: Emergent Spatial and Spatiotemporal Patterns by Taylor, Nick P., Kim, Hyunyeon, Krause, Andrew L., Van Gorder, Robert A.

“…We extend a spatially non-local cross-diffusion model of aggregation between multiple species with directed motion toward resource gradients to include many…”
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