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Articles 1 - 16 of 16
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.
Locust Dynamics: Behavioral Phase Change And Swarming, Chad M. Topaz, Maria R. D'Orsogna, Leah Edelstein-Keshet, Andrew J. Bernoff
Locust Dynamics: Behavioral Phase Change And Swarming, Chad M. Topaz, Maria R. D'Orsogna, Leah Edelstein-Keshet, Andrew J. Bernoff
Chad M. Topaz
Locusts exhibit two interconvertible behavioral phases, solitarious and gregarious. While solitarious individuals are repelled from other locusts, gregarious insects are attracted to conspecifics and can form large aggregations such as marching hopper bands. Numerous biological experiments at the individual level have shown how crowding biases conversion towards the gregarious form. To understand the formation of marching locust hopper bands, we study phase change at the collective level, and in a quantitative framework. Specifically, we construct a partial integrodifferential equation model incorporating the interplay between phase change and spatial movement at the individual level in order to predict the dynamics of …
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.
Asymptotic Dynamics Of Attractive-Repulsive Swarms, Andrew Leverentz, Chad M. Topaz, Andrew J. Bernoff
Asymptotic Dynamics Of Attractive-Repulsive Swarms, Andrew Leverentz, Chad M. Topaz, Andrew J. Bernoff
Chad M. Topaz
We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the density with a kernel describing attractive-repulsive social interactions. The kernel's first moment and its limiting behavior at the origin determine whether the population asymptotically spreads, contracts, or reaches steady-state. For the spreading case, the dynamics approach those of the porous medium equation. The widening, compactly-supported population has edges that behave like traveling waves whose speed, density and slope we calculate. For the …
A Model For Rolling Swarms Of Locusts, Chad M. Topaz, Andrew J. Bernoff, Sheldon Logan, Wyatt Toolson
A Model For Rolling Swarms Of Locusts, Chad M. Topaz, Andrew J. Bernoff, Sheldon Logan, Wyatt Toolson
Chad M. Topaz
We construct an individual-based kinematic model of rolling migratory locust swarms. The model incorporates social interactions, gravity, wind, and the effect of the impenetrable boundary formed by the ground. We study the model using numerical simulations and tools from statistical mechanics, namely the notion of H-stability. For a free-space swarm (no wind and gravity), as the number of locusts increases, the group approaches a crystalline lattice of fixed density if it is H-stable, and in contrast becomes ever denser if it is catastrophic. Numerical simulations suggest that whether or not a swarm rolls depends on the statistical mechanical properties of …
Modeling The Potential Impact Of Rectal Microbicides To Reduce Hiv Transmission In Bathhouses, Romulus Breban, Ian Mcgowan, Chad M. Topaz, Elissa Schwartz, Peter Anton, Sally Blower
Modeling The Potential Impact Of Rectal Microbicides To Reduce Hiv Transmission In Bathhouses, Romulus Breban, Ian Mcgowan, Chad M. Topaz, Elissa Schwartz, Peter Anton, Sally Blower
Chad M. Topaz
We evaluate the potential impact of rectal microbicides for reducing HIV transmission in bathhouses. A new mathematical model describing HIV transmission dynamics among men who have sex with men (MSM) in bathhouses is constructed and analyzed. The model incorporates key features affecting transmission, including sexual role behavior (insertive and receptive anal intercourse acts), biological transmissibility of HIV, frequency and efficacy of condom usage, and, most pertinently, frequency and efficacy of rectal microbicide usage. To evaluate the potential impact of rectal microbicide usage, we quantify the effect of rectal microbicides (ranging in efficacy from 10% to 90%) on reducing the number …
A Nonlocal Continuum Model For Biological Aggregations, Chad M. Topaz, Andrea L. Bertozzi, Mark E. Lewis
A Nonlocal Continuum Model For Biological Aggregations, Chad M. Topaz, Andrea L. Bertozzi, Mark E. Lewis
Chad M. Topaz
We construct a continuum model for biological aggregations in which individuals experience long-range social attraction and short range dispersal. For the case of one spatial dimension, we study the steady states analytically and numerically. There exist strongly nonlinear states with compact support and steep edges that correspond to localized biological aggregations, or clumps. These steady state clumps are approached through a dynamic coarsening process. In the limit of large population size, the clumps approach a constant density swarm with abrupt edges. We use energy arguments to understand the nonlinear selection of clump solutions, and to predict the internal density in …
Swarming Patterns In A Two-Dimensional Kinematic Model For Biological Groups, Chad M. Topaz, Andrea L. Bertozzi
Swarming Patterns In A Two-Dimensional Kinematic Model For Biological Groups, Chad M. Topaz, Andrea L. Bertozzi
Chad M. Topaz
We construct a continuum model for the motion of biological organisms experiencing social interactions and study its pattern-forming behavior. The model takes the form of a conservation law in two spatial dimensions. The social interactions are modeled in the velocity term, which is nonlocal in the population density and includes a parameter that controls the interaction length scale. The dynamics of the resulting partial integrodifferential equation may be uniquely decomposed into incompressible motion and potential motion. For the purely incompressible case, the model resembles one for fluid dynamical vortex patches. There exist solutions which have constant population density and compact …
Multifrequency Control Of Faraday Wave Patterns, Chad M. Topaz, Jeff Porter, Mary Silber
Multifrequency Control Of Faraday Wave Patterns, Chad M. Topaz, Jeff Porter, Mary Silber
Chad M. Topaz
We show how pattern formation in Faraday waves may be manipulated by varying the harmonic content of the periodic forcing function. Our approach relies on the crucial influence of resonant triad interactions coupling pairs of critical standing wave modes with damped, spatiotemporally resonant modes. Under the assumption of weak damping and forcing, we perform a symmetry-based analysis that reveals the damped modes most relevant for pattern selection, and how the strength of the corresponding triad interactions depends on the forcing frequencies, amplitudes, and phases. In many cases, the further assumption of Hamiltonian structure in the inviscid limit determines whether the …
Pattern Control Via Multi-Frequency Parametric Forcing, Jeff Porter, Chad M. Topaz, Mary Silber
Pattern Control Via Multi-Frequency Parametric Forcing, Jeff Porter, Chad M. Topaz, Mary Silber
Chad M. Topaz
We use symmetry considerations to investigate control of a class of resonant three-wave interactions relevant to pattern formation in weakly damped, parametrically forced systems near onset. We classify and tabulate the most important damped, resonant modes and determine how the corresponding resonant triad interactions depend on the forcing parameters. The relative phase of the forcing terms may be used to enhance or suppress the nonlinear interactions. We compare our symmetry-based predictions with numerical and experimental results for Faraday waves. Our results suggest how to design multifrequency forcing functions that favor chosen patterns in the lab.
Fractional Bandwidth Reacquisition Algorithms For Vsw-Mcm, Ben Cook, Daniel Marthaler, Chad M. Topaz, Andrea L. Bertozzi, Mathieu Kemp
Fractional Bandwidth Reacquisition Algorithms For Vsw-Mcm, Ben Cook, Daniel Marthaler, Chad M. Topaz, Andrea L. Bertozzi, Mathieu Kemp
Chad M. Topaz
Autonomous underwater vehicles are gradually being recognized as key assets in future combat systems. Central to this attitude is the realization that teams of vehicles acting in concerted fashion can accomplish tasks that are either too costly or simply outside the range of capabilities of single vehicles. The VSW-MCM target reacquisition problem is the primary driver of underwater multi-agent research. Because of the VSW's inherent high vehicle attrition rate and unreliable communication, it is felt that vehicle coordination must be done off-site. In this paper, we suggest an alternative to this which permits on-site coordination despite loss of vehicles and …
Resonances And Superlattice Pattern Stabilization In Two-Frequency Forced Faraday Wave, Chad M. Topaz, Mary Silber
Resonances And Superlattice Pattern Stabilization In Two-Frequency Forced Faraday Wave, Chad M. Topaz, Mary Silber
Chad M. Topaz
We investigate the role weakly damped modes play in the selection of Faraday wave patterns forced with rationally related frequency components $m\omega$ and $n\omega$. We use symmetry considerations to argue for the special importance of the weakly damped modes oscillating with twice the frequency of the critical mode, and those oscillating primarily with the “difference frequency” $|n−m| \omega$ and the “sum frequency” $(n+m) \omega$. We then perform a weakly nonlinear analysis using equations of Zhang and Viñals [J. Fluid Mech. 336 (1997) 301] which apply to small-amplitude waves on weakly inviscid, deep fluid layers. For weak damping and forcing and …
Two-Frequency Forced Faraday Waves: Weakly Damped Modes And Pattern Selection, Mary Silber, Chad M. Topaz, Anne Skeldon
Two-Frequency Forced Faraday Waves: Weakly Damped Modes And Pattern Selection, Mary Silber, Chad M. Topaz, Anne Skeldon
Chad M. Topaz
Recent experiments [A. Kudrolli, B. Pier, J.P. Gollub, Physica D 123 (1998) 99–111] on two-frequency parametrically excited surface waves produce an intriguing "superlattice" wave pattern near a codimension-two bifurcation point where both subharmonic and harmonic waves onset simultaneously, but with different spatial wavenumbers. The superlattice pattern is synchronous with the forcing, spatially periodic on a large hexagonal lattice, and exhibits small-scale triangular structure. Similar patterns have been shown to exist as primary solution branches of a generic 12-dimensional ${\rm D}_6\dot{+}{\rm T}^2$-equivariant bifurcation problem, and may be stable if the nonlinear coefficients of the bifurcation problem satisfy certain inequalities [M. Silber, …