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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)
We present the second of two articles on the small volume-fraction limit of a nonlocal Cahn–Hilliard functional introduced to model microphase separation of diblock copolymers. After having established the results for the sharp-interface version of the functional [SIAM we consider here the full diffuse-interface functional and address the limit in which ε(More)
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 use a local energy method to study the spatial localization of the supports of the solutions of a reaction{ diiusion system with nonlinear diiusion and a general reaction term. We establish nite speed of propagation and the existence of waiting times under a set of weak assumptions on the structural form of the system. These assumptions allow for(More)
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 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)
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)
We study the minima of the functional R f (ru). The function f is not convex, the set is a domain in R 2 and the minimum is sought over all convex functions on with values in a given bounded interval. We prove that u is almost everywherèon the boundary of convexity', in the sense that there exists no open set on which u is both strictly convex and(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)