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2005-01-01

Frithjof Lutscher, Elizaveta Pachepsky, Mark A. Lewis

Individuals in streams are constantly subject to predominantly unidirectional flow. The question of how these populations can persist in upper stream reaches is known as the “drift paradox.” We employ a general mechanistic movement-model framework and derive dispersal kernels for this situation....

2002

Kouritzin, Michael, Long, H.

In the context of simulating the transport of a chemical or bacterial contaminant through a moving sheet of water, we extend a well-established method of approximating reaction-diffusion equations with Markov chains by allowing convection, certain Poisson measure driving sources and a larger...

1995-01-01

Sherratt, J. A., Lewis, Mark A., Fowler, A. C.

Irregularities in observed population densities have traditionally been attributed to discretization of the underlying dynamics. We propose an alternative explanation by demonstrating the evolution of spatiotemporal chaos in reaction-diffusion models for predator-prey interactions. The chaos is...

2013

Kouritzin, Michael, Wu, B., Newton, F.

Herein, we propose generating CAPTCHAs through random field simulation and give a novel, effective and efficient algorithm to do so. Indeed, we demonstrate that sufficient information about word tests for easy human recognition is contained in the site marginal probabilities and the...

1992

Kouritzin, Michael, Heunis, A.J.

Let μ be a positive finite Borel measure on the real line R. For t ≥ 0 let et · E1 and E2 denote, respectively, the linear spans in L2(R, μ) of {eisx, s > t} and {eisx, s < 0}. Let θ: R → C such that ∥θ∥ = 1, denote by αt(θ, μ) the angle between θ · et · E1 and E2. The problems considered here...

2018-10-23

Niewenhuis et al.

The dynamics of a fully nonlinear, tree-structured resonator and its response to a broadband forcing of the branches is examined. It is shown that the broadband forcing yields a transfer of energy between the parts of the spectrum so that the spectrum becomes progressively more narrow-band for...

2011-01-01

Fagan, W. F., Jin, Y., Bishop, J. G., Marleau, J. M., Lewis, Mark A.

The relative importance of plant facilitation and competition during primary succession depends on the development of ecosystem nutrient pools, yet the interaction of these processes remains poorly understood. To explore how these mechanisms interact to drive successional dynamics, we devised a...

2012-01-01

Ashander, Jaime, Lewis, Mark A., Krkošek, Martin

Exchange of diseases between domesticated and wild animals is a rising concern for conservation. In the ocean, many species display life histories that separate juveniles from adults. For pink salmon (Oncorhynchus gorbuscha) and parasitic sea lice (Lepeophtheirus salmonis), infection of juvenile...

2008-01-01

Potapov, A. B., Lewis, Mark A.

We consider the model of invasion prevention in a system of lakes that are connected via traffic of recreational boats. It is shown that, in presence of an Allee effect, the general optimal control problem can be reduced to a significantly simpler stationary optimization problem of optimal...

2006-01-01

Chad M. Topaz, Andrea L. Bertozzi, Mark A. Lewis

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...