Related papers: Elastic curves and surfaces under long-range force…

We study deformation theory of elliptic fibre bundles over curves in positive characteristics. As applications, we give examples of non-liftable elliptic surfaces in charactertic two and three, which answers a question of Katsura and Ueno.…

Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a…

Based on the superposition of incremental frictional surface tractions that, in the case of an incompressible elastic half-space, correspond to a rigid tangential translation of a circular contact domain, the stress and displacement fields…

Thin surfaces are ubiquitous in nature, from leaves to cell membranes, and in technology, from paper to corrugated containers. Structural thinness imbues them with flexibility, the ability to easily bend under light loads, even as their…

We provide a new angle and obtain new results on a class of metrics on length-normalized curves in $d$ dimensions, represented by their unit tangents expressed as a function of arc-length, which are functions from the unit interval to the…

Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in finite samples. These general expressions are valid for anisotropic media as well. Specifically for the…

Experimentally measuring the elastic properties of thin biological surfaces is non-trivial, particularly when they are curved. One technique that may be used is the indentation of a thin sheet of material by a rigid indenter, whilst…

We put forward a variational framework suitable for the study of curves whose energies depend on their bend and twist degrees of freedom. By employing the material curvatures to describe such elastic deformation modes, we derive the…

The boundary conditions at the deformable interface between two contacting fluids are derived for the general case of the large-amplitude perturbations. The interface is modeled as perturbed free boundary that evolves in time, and the…

Under analysis is travel of P-waves in an elastic pipe partly embedded in soil with dry friction. The mathematical formulation of the problem on impact pipe driving in soil is based on the model of axial vibration of an elastic bar,…

An instantaneous sub-surface disturbance in a two-dimensional elastic half-space is considered. The disturbance propagates through the elastic material until it reaches the free surface, after which it propagates out along the surface. In…

We derive integral and sup-estimates for the curvature of stably marginally outer trapped surfaces in a sliced space-time. The estimates bound the shear of a marginally outer trapped surface in terms of the intrinsic and extrinsic curvature…

We consider the steady-state analysis of a pinned elastic plate lying on the free surface of a thin viscous fluid, forced by the motion of a bottom substrate moving at constant speed. A mathematical model incorporating elasticity,…

Understanding the contact between rough surfaces undergoing plastic deformation is crucial in many applications. We study the effect of plastic deformation on the surface separation between two solids with random roughness. Assuming a…

Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in three dimensional, not necessarily isotropic, finite samples. A line integral representation is found for…

Adhesive contact between a thin elastic sheet and a substrate in a liquid environment arises in a range of biological, physical and technological applications. By considering the dynamics of this process that naturally couples fluid flow,…

Wrinkling of stretched elastic sheets is widely observed, and the scaling relations between the amplitude and wavelength of the wrinkles have been proposed by Cerda and Mahadevan. However, the surface effects should be taken into account…

Non-relativistic particles that are effectively confined to two dimensions can in general move on curved surfaces, allowing dynamical phenomena beyond what can be described with scalar potentials or even vector gauge fields. Here we…

We consider the forced motion of a relativistic particle constrained on a curve and present sufficient conditions for periodic oscillations by means of an illustrative geometrical approach. Obtained result is illustrated by a few examples…

This article deals with flow of plane curves driven by the curvature and external force. We make use of such a geometric flow for the purpose of image segmentation. A parametric model for evolving curves with uniform and curvature adjusted…