Related papers: Reshaping of a Janus ring
Stability of solitary waves in a thin inextensible and unshearable rod of infinite length is studied. Solitary-wave profile ofthe elastica of such a rod without torsion has the form of a planar loop and its speed depends on a tension in the…
Using a recently derived filament model, the stability of fluid filaments in Hele-Shaw cells, driven by a constant pressure gradient, is studied. It is found that thin circular filaments grow if their initial radius exceeds a dimensionless…
A creased thin disk is generally bistable since the crease could be pushed through to form a stable cone-like inverted state with an elastic singularity corresponding to the vertex of the conical surface. In a recent study, we found that…
An experimental method has been developed to locate unstable equilibria of nonlinear structures quasi-statically. The technique involves loading a structure by application of either a force or a displacement at a main actuation point, while…
A dielectric elastomer whose edges are held fixed will buckle, given sufficient applied voltage, resulting in a nontrivial out-of-plane deformation. We study this situation numerically using a nonlinear elastic model which decouples two of…
A variational framework is developed to examine the equilibrium states of a semi-flexible polymer that is constrained to lie on a fixed surface. As an application the confinement of a closed polymer loop of fixed length $2\pi R$ within a…
Jamming is a phenomenon occurring in systems as diverse as traffic, colloidal suspensions and granular materials. A theory on the reversible elastic deformation of jammed states is presented. First, an explicit granular stress-strain…
The prediction of the temporal dynamics of chaotic systems is challenging because infinitesimal perturbations grow exponentially. The analysis of the dynamics of infinitesimal perturbations is the subject of stability analysis. In stability…
The stability of static uncharged spheres with anisotropic internal stresses is studied in general relativity. It has been noticed that pressure anisotropy plays an important role for stability of stellar structure. It is shown that radial…
This paper proposes a new approach to describe the stability of linear time-invariant systems via the torsion $\tau(t)$ of the state trajectory. For a system $\dot{r}(t)=Ar(t)$ where $A$ is invertible, we show that (1) if there exists a…
Rotating the clamped ends of a buckled elastica induces a snap-through instability. Predicting the limit point and determining the equilibria at the start and end of the snap are routine computations in the quasi-static setting. The…
A system of $n$ screw dislocations in an isotropic crystal undergoing antiplane shear is studied in the framework of linear elasticity. Imposing a suitable boundary condition for the strain, namely requesting the non-vanishing of its…
We model within the framework of finite elasticity two inherent instabilities observed in liquid crystal elastomers under uniaxial tension. First is necking which occurs when a material sample suddenly elongates more in a small region where…
We study the equilibrium configurations related to the growth of an elastic fibre in a confining flexible ring. This system represents a paradigm for a variety of biological, medical, and engineering problems. We consider a simplified…
A thin flat rectangular plate supported on its edges and subjected to in-plane loading exhibits stable post-buckling behaviour. However, the introduction of a nonlinear (softening) elastic foundation may cause the response to become…
Polarized ferrofluids, lipid monolayers and magnetic bubbles form domains with deformable boundaries. Stability analysis of these domains depends on a family of nontrivial integrals. We present a closed form evaluation of these integrals as…
This paper presents a theoretical study of oscillatory and rotational instabilities of a solid spherical body, levitated electromagnetically in axisymmetric coils made of coaxial circular loops. We apply our previous theory to analyze the…
Deformations of heavy elastic cylinders with their axis in the direction of earth's gravity field are investigated. The specimens, made of polyacrylamide hydrogels, are attached from their top circular cross section to a rigid plate. An…
The population model of Busenberg and Travis is a paradigmatic model in ecology and tumour modelling due to its ability to capture interesting phenomena like the segregation of populations. Its singular mathematical structure enforces the…
A simple kinetic model of a two-component deformable and reactive bilayer is presented. The two differently shaped components are interconverted by a nonequilibrium reaction, and a phenomenological coupling between local composition and…