Related papers: Circular and helical equilibrium solutions of inho…
Helical configurations of inhomogeneous symmetric rods with non-constant bending and twisting stiffness are studied within the framework of the Kirchhoff rod model. From the static Kirchhoff equations, we obtain a set of differential…
The tridimensional configuration and the twist density of helical rods with varying cross section radius are studied within the framework of the Kirchhoff rod model. It is shown that the twist density increases when the cross section radius…
We study slender, helical elastic rods subject to distributed forces and moments. Focussing on the case when the helix axis remains straight, we employ the method of multiple scales to systematically derive an 'equivalent-rod' theory from…
The Kirchhoff-Plateau problem concerns the equilibrium shapes of a system in which a flexible filament in the form of a closed loop is spanned by a liquid film, with the filament being modeled as a Kirchhoff rod and the action of the…
We present a new exact solution for the twist of an asymmetric thin elastic rods. The shape of such rods is described by the static Kirchhoff equations. In the case of constant curvatire and torsion the twist of the asymmetric rod…
The equilibrium of magneto-elastic rods, formed of an elastic matrix containing a uniform distribution of paramagnetic particles, that are subject to terminal loads and are immersed in a uniform magnetic field, is studied. The deduced…
The stability of the multiple equilibrium states of a hexagram ring with six curved sides is investigated. Each of the six segments is a rod having the same length and uniform natural curvature. These rods are bent uniformly in the plane of…
The Kirchhoff model describes the statics and dynamics of thin rods within the approximations of the linear elasticity theory. In this paper we develop a method, based on a shooting technique, to find equilibrium configurations of finite…
The Kirchhoff's theory for thin, inextensible, elastic rods with nonhomogeneous cross section is studied. The Young's and shear moduli of the rod are considered to vary radially, and it is shown that an analytical solution for the…
The Kirchhoff elastic theory of thin filaments with spontaneous curvature is employed in the understanding of the onset of the kink transitions observed in short DNA rings. Dynamical analysis shows that when its actual curvature is less…
We consider the equilibrium shapes of a thin, annular strip cut out in an elastic sheet. When a central fold is formed by creasing beyond the elastic limit, the strip has been observed to buckle out-of-plane. Starting from the theory of…
The equations for the equilibrium of a thin elastic ribbon are derived by adapting the classical theory of thin elastic rods. Previously established ribbon models are extended to handle geodesic curvature, natural out-of-plane curvature,…
In this paper we study concentrated solutions of the three-dimensional Euler equations in helical symmetry without swirl. We prove that any helical vorticity solution initially concentrated around helices of pairwise distinct radii remains…
We consider the Euler equations in ${\mathbb R}^3$ expressed in vorticity form. A classical question that goes back to Helmholtz is to describe the evolution of solutions with a high concentration around a curve. The work of Da Rios in 1906…
We investigate the stability of a uniform elliptical vortex in a two-dimensional incompressible Euler fluid. It's demonstrated that for small eccentricities, the vortex relaxes to a core-halo structure that undergoes rigid rotation with the…
A XY Heisenberg spin chain model with two perpendicular spins par site is mapped onto a Kirchhoff thin elastic rod. It is shown that in the case of constant curvature the Euler--Lagrange equation leads to the static sine-Gordon equation.…
Helices are not generic outcomes of polymer collapse. Collapsed conformations of semiflexible polymers with isotropic attractions typically form globules, toroids, or rod-like structures, as seen in simulations and described by…
Kinetic helicity is one of the invariants of the Euler equations that is associated with the topology of vortex lines within the fluid. In superfluids, the vorticity is concentrated along vortex filaments. In this setting, helicity would be…
We consider reshaping of closed Janus filaments acquiring intrinsic curvature upon actuation of an active component -- a nematic elastomer elongating upon phase transition. Linear stability analysis establishes instability thresholds of…
We study the three-dimensional static configurations of nonhomogeneous Kirchhoff filaments with periodically varying Young's modulus. This type of variation may occur in long tandemly repeated sequences of DNA. We analyse the effects of the…