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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)
A long structural system with an unstable (subcritical) post-buckling response that subsequently restabil-izes 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(More)
We study a one-dimensional continuum model for lipid bilayers. The system consists of water and lipid molecules; lipid molecules are represented by two 'beads', a head bead and a tail bead, connected by a rigid rod. We derive a simplified model for such a system, in which we only take into account the effects of entropy and hydrophilic/hydrophobic(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)
Kink banding, common to many structures in nature and engineering, has several distinctive featuresÐnotably highly non-linear 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 e€ects of lesser immediate(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)