Mark A. Peletier

Cellular buckling in long structures

A long structural system with an unstable (subcritical)post-buckling response that subsequently restabilizes typically deformsin a cellular manner, with localized buckles first forming and thenlocking up in sequence. As buckling continues over a growing number ofcells, the response can be described by a set of lengthening homoclinicconnections from the fundamental equilibrium state to itself. In thelimit, this leads to a heteroclinic connection from the fundamentalunbuckled state to a post-buckled state that is periodic. Under suchprogressive displacement the load tends to oscillate between twodistinct values.The paper is both a review and a pointer tofuture research. The response is described via a typical system, asimple but ubiquitous model of a strut on a foundation which includesinitially-destabilizing and finally-restabilizing nonlinear terms. Anumber of different structural forms, including the axially-compressedcylindrical shell, a typical sandwich structure, a model of geologicalfolding and a simple link model are shown to display such behaviour. Amathematical variational argument is outlined for determining the globalminimum postbuckling state under controlled end displacement (rigidloading). Finally, the paper stresses the practical significance of aMaxwell-load instability criterion for such systems. This criterion,defined under dead loading to be where the pre-buckled and post-buckledstate have the same energy, is shown to have significance in the presentsetting under rigid loading also. Specifically, the Maxwell load isargued to be the limit of minimum energy localized solutions asend-shortening tends to infinity.

A chaotic self-oscillating sunlight-driven polymer actuator

Nature provides much inspiration for the design of materials capable of motion upon exposure to external stimuli, and many examples of such active systems have been created in the laboratory. However, to achieve continuous motion driven by an unchanging, constant stimulus has proven extremely challenging. Here we describe a liquid crystalline polymer film doped with a visible light responsive fluorinated azobenzene capable of continuous chaotic oscillatory motion when exposed to ambient sunlight in air. The presence of simultaneous illumination by blue and green light is necessary for the oscillating behaviour to occur, suggesting that the dynamics of continuous forward and backward switching are causing the observed effect. Our work constitutes an important step towards the realization of autonomous, persistently self-propelling machines and self-cleaning surfaces powered by sunlight.

On the Phase Diagram for Microphase Separation of Diblock Copolymers: An Approach via a Nonlocal Cahn–Hilliard Functional

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 phase plane. That is, we divide the plane into regions wherein a combination of analysis and numerics is used to describe minimizers. In particular we identify a regime wherein the uniform (disordered state) is the unique global minimizer; a regime wherein the constant state is linearly unstable and where numerical simulations are currently the only tool for characterizing the phase geometry; and a regime of small volume fraction wherein we conjecture that small well-separated approximately spherical objects are the unique global minimizer. For this last regime, we present an asymptotic analysis from the point of view of the energetics which will be comp...

Newton's Problem of the Body of Minimal Resistance in the Class of Convex Developable Functions

We investigate the minimization of Newtons functional for the problem of the body of minimal resistance with maximal height

The Maxwell stability criterion in pseudo-energy models of kink banding

{M>0

Asymptotic behaviour of a pile-up of infinite walls of edge dislocations

cite{butt 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 cite{lrp2. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with~

Control of spatially heterogeneous and time-varying cellular reaction networks: a new summation law.

n

GENERIC formalism of a Vlasov–Fokker–Planck equation and connection to large-deviation principles

sides centered in the disc, and numerical experiments indicate that the natural number

Cylinder Buckling: The Mountain Pass as an Organizing Center

ngeq2

Why the Phosphotransferase System of Escherichia coli Escapes Diffusion Limitation

is a non-decreasing function of