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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Social Aggregation In Pea Aphids: Experiment And Random Walk Modeling, Christa Nilsen, John Paige, Olivia Warner, Benjamin Mayhew, Ryan Sutley, Mathew Lam, Andrew J. Bernoff, Chad M. Topaz
Social Aggregation In Pea Aphids: Experiment And Random Walk Modeling, Christa Nilsen, John Paige, Olivia Warner, Benjamin Mayhew, Ryan Sutley, Mathew Lam, Andrew J. Bernoff, Chad M. Topaz
Chad M. Topaz
No abstract provided.
Instabilities And Patterns In Coupled Reaction-Diffusion Layers, Anne J. Catlla, Amelia Mcnamara, Chad M. Topaz
Instabilities And Patterns In Coupled Reaction-Diffusion Layers, Anne J. Catlla, Amelia Mcnamara, Chad M. Topaz
Chad M. Topaz
We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer systems of identical two-component reactions, we analyze the stability of homogeneous steady states by exploiting the block symmetric structure of the linear problem. There are eight possible primary bifurcation scenarios, including a Turing-Turing bifurcation that involves two disparate length scales whose ratio may be tuned via the interlayer coupling. For systems of n-component layers and nonidentical layers, the linear problem’s block form allows approximate decomposition into lower-dimensional linear problems if the coupling is sufficiently weak. As an example, we apply these results to a two-layer …
A Primer Of Swarm Equilibria, Andrew J. Bernoff, Chad M. Topaz
A Primer Of Swarm Equilibria, Andrew J. Bernoff, Chad M. Topaz
Chad M. Topaz
We study equilibrium configurations of swarming biological organisms subject to exogenous and pairwise endogenous forces. Beginning with a discrete dynamical model, we derive a variational description of the corresponding continuum population density. Equilibrium solutions are extrema of an energy functional, and satisfy a Fredholm integral equation. We find conditions for the extrema to be local minimizers, global minimizers, and minimizers with respect to infinitesimal Lagrangian displacements of mass. In one spatial dimension, for a variety of exogenous forces, endogenous forces, and domain configurations, we find exact analytical expressions for the equilibria. These agree closely with numerical simulations of the underlying …
Forced Patterns Near A Turing-Hopf Bifurcation, Chad M. Topaz, Anne Catlla
Forced Patterns Near A Turing-Hopf Bifurcation, Chad M. Topaz, Anne Catlla
Chad M. Topaz
We study time-periodic forcing of spatially-extended patterns near a Turing-Hopf bifurcation point. A symmetry-based normal form analysis yields several predictions, including that (i) weak forcing near the intrinsic Hopf frequency enhances or suppresses the Turing amplitude by an amount that scales quadratically with the forcing strength, and (ii) the strongest effect is seen for forcing that is detuned from the Hopf frequency. To apply our results to specific models, we perform a perturbation analysis on general two-component reaction-diffusion systems, which reveals whether the forcing suppresses or enhances the spatial pattern. For the suppressing case, our results explain features of previous …
Review Of “Continuum Modeling In The Physical Sciences” By Van Groesen And Molenaar, Chad M. Topaz
Review Of “Continuum Modeling In The Physical Sciences” By Van Groesen And Molenaar, Chad M. Topaz
Chad M. Topaz
No abstract provided.