Related papers: Elastic curves and surfaces under long-range force…
Soft interfaces can mediate interactions between particles bound to them. The force transmitted through the surface geometry on a particle may be expressed as a closed line integral of the surface stress tensor around that particle. This…
We revisit the classical problem of the planar Euler \emph{elastica} with applied forces and moments, and present a classification of the shapes in terms of tangentially conserved quantities associated with spatial and material symmetries.…
Thin elastic sheets appear in systems ranging from graphene to biological membranes, where phenomena such as wrinkling, folding, and thermal fluctuations originate from geometric nonlinearities. These effects are treated within weakly…
The paper presents a reformulation of some of the most basic entities and equations of linear elasticity - the stress and strain tensor, the Cauchy Navier equilibrium equations, material equations for linear isotropic bodies - in a modern…
We perform a variational analysis of an elastic membrane spanning a closed curve which may sustain bending and torsion. First, we deal with parametrized curves and linear elastic membranes proving the existence of equilibria and finding…
In arXiv:2205.02920 a variant of the classical elastic flow for closed curves in $\mathbb{R}^{n}$ was introduced, that is more suitable for numerical purposes. Here we investigate the long-time properties of such evolution demonstrating…
The curvature potential arising from confining a particle initially in three-dimensional space onto a curved surface is normally derived in the hard constraint $q \to 0$ limit, with $q$ the degree of freedom normal to the surface. In this…
The problem of a disc and a ball rolling on a horizontal plane without slipping is considered. Differential constrained equations are shown to be integrated when the trajectory of the point of contact is taken in a form of the natural…
Within the framework of nonrelativistic electrodynamics, general formulas have been obtained for the tangential dissipative force of electrostatic friction and the normal force of attraction to the surface of an axially symmetric probe…
The elastica is a curve in $\R^3$ that is stationary under variations of the integral of the square of the curvature. Elastica is viewed as a dynamical system that arises from the second order calculus of variations, and its quantization is…
In this paper, we investigate the geometric invariant properties of a normal curve on a smooth immersed surface under conformal transformation. We obtain an invariant-sufficient condition for the conformal image of a normal curve. We also…
Differentiable physics is a powerful approach to learning and control problems that involve physical objects and environments. While notable progress has been made, the capabilities of differentiable physics solvers remain limited. We…
The relation between the elastic wave equation for plane, isotropic bodies and an underlying classical ray dynamics is investigated. We study in particular the eigenfrequencies of an elastic disc with free boundaries and their connection to…
Motivated by a problem posed by David A. Singer in 1999 and by the elastic spherical curves, we study the spherical curves whose curvature is expressed in terms of the distance to a great circle (or from a point). By introducing the notion…
We derive the Pauli equation for a charged spin particle confined to move on a spatially curved surface $\mathcal{S}$ in an electromagnetic field. Using the thin-layer quantization scheme to constrain the particle on $\mathcal{S}$, and in…
The motion of an object within a viscous fluid and in the vicinity of a soft surface induces a hydrodynamic stress field that deforms the latter, thus modifying the boundary conditions of the flow. This results in elastohydrodynamic (EHD)…
Motivated by the power of subregion/subregion duality for constraining the bulk geometry in gauge/gravity duality, we pursue a comprehensive and systematic approach to the behavior of extremal surfaces under perturbations. Specifically, we…
In this paper, we consider the classical variational problem in the Galilean space. we develop the Euler-Lagrange equations for a elastic line on an oriented surface in the Galilean 3-dimensional space $G_3$. Using the varia- tion method,…
We propose a phenomenological equation to describe kinetic roughening of a growing surface in presence of long range interactions. The roughness of the evolving surface depends on the long range feature, and several distinct scenarios of…
The electrostatic force on a spherical particle near a planar surface is calculated for the cases of a uniform electric field applied in either normal or tangential direction to the surface. The particle and suspending media are assumed to…