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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 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 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 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)
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)