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A long structural system with an unstable (subcritical) post-buckling response that subsequently restabilizes typically deforms in a cellular manner, with localized buckles first forming and then locking up in sequence. As buckling continues over a growing number of cells, the response can be described by a set of lengthening homoclinic connections from the… (More)

- Rustum Choksi, Mark A. Peletier
- SIAM J. Math. Analysis
- 2010

We present the first of two articles on the small volume fraction limit of a nonlocal Cahn–Hilliard functional introduced to model microphase separation of diblock copolymers. Here we focus attention on the sharp-interface version of the functional and consider a limit in which the volume fraction tends to zero but the number of minority phases (called… (More)

- Rustum Choksi, Mark A. Peletier, J. F. Williams
- SIAM Journal of Applied Mathematics
- 2009

We consider analytical and numerical aspects of the phase diagram for microphase separation of diblock copolymers. Our approach is variational and is based upon a density functional theory which entails minimization of a nonlocal Cahn–Hilliard functional. Based upon two parameters which characterize the phase diagram, we give a preliminary analysis of the… (More)

We study a variational model for a diblock-copolymer/homopolymer blend. The energy functional is a sharp-interface limit of a generalisation of the Ohta-Kawasaki energy. In one dimension, on the real line and on the torus, we prove existence of minimisers of this functional and we describe in complete detail the structure and energy of stationary points.… (More)

Kink banding, common to many structures in nature and engineering, has several distinctive featuresÐnotably highly nonlinear snap-back instability leading to localization and sequential lock-up. The proposed friction model, although simpli®ed, introduces these de®ning characteristics without obscuring them by including other eects of lesser immediate… (More)

- Mark A. Peletier, Hans V. Westerhoff, Boris N. Kholodenko
- Journal of theoretical biology
- 2003

A hallmark of a plethora of intracellular signaling pathways is the spatial separation of activation and deactivation processes that potentially results in precipitous gradients of activated proteins. The classical metabolic control analysis (MCA), which quantifies the influence of an individual process on a system variable as the control coefficient,… (More)

We investigate the minimization of Newton’s functional for the problem of the body of minimal resistance with maximal height M > 0 [1] in the class of convex developable functions defined in a disc. This class is a natural candidate to find a (non-radial) minimizer in accordance with the results of [2]. We prove that the minimizer in this class has a… (More)

- Robert Planqué, Nicholas F. Britton, Nigel R. Franks, Mark A. Peletier
- Bulletin of mathematical biology
- 2002

Host bird species of the Eurasian Cuckoo, Cuculus canorus, often display egg-discrimination behaviour but chick-rejection behaviour has never been reported. In this paper, we analyse a host-cuckoo association in which both population dynamics and evolutionary dynamics are explored in a discrete-time model. We introduce four host types, each with their own… (More)

- Mark A. Peletier, Giuseppe Savaré, Marco Veneroni
- SIAM J. Math. Analysis
- 2010

We study the limit of high activation energy of a special Fokker–Planck equation known as the Kramers–Smoluchowski equation (KS). This equation governs the time evolution of the probability density of a particle performing a Brownian motion under the influence of a chemical potential H/ε. We choose H having two wells corresponding to two chemical states A… (More)

We study a singular-limit problem arising in the modelling of chemical reactions. At finite ε > 0, the system is described by a Fokker-Planck convection-diffusion equation with a double-well convection potential. This potential is scaled by 1/ε, and in the limit ε→ 0, the solution concentrates onto the two wells, resulting into a limiting system that is a… (More)