Related papers: Elastica as a dynamical system
Elastic turbulence can lead to to increased flow resistance, mixing and heat transfer. Its control -- either suppression or promotion -- has significant potential, and there is a concerted ongoing effort by the community to improve our…
We present the general theory of Ising transitions in isotropic elastic media with vanishing thermal expansion. By constructing a minimal model with appropriate spin-lattice couplings, we show that in two dimensions near a continuous…
Relativistic elasticity on an arbitrary spacetime is formulated as a Lagrangian field theory which is covariant under spacetime diffeomorphisms. This theory is the relativistic version of classical elasticity in the hyperelastic, materially…
We report the counter-intuitive instability of charged elastic rings, and the persistence of sinusoidal deformations in the lowest-energy configurations by the combination of high-precision numerical simulations and analytical perturbation…
We discuss the role of elastic stress in the statistical properties of elastic turbulence, realized by the flow of a polymer solution between two disks. The dynamics of the elastic stress are analogous to those of a small scale fast dynamo…
When a system has more than one stable state, how can the stability of these states be compared? This deceptively simple question has important consequences for ecosystems, because systems with alternative stable states can undergo dramatic…
An interface description and numerical simulations of model A kinetics are used for the first time to investigate the intra-surface kinetics of phase ordering on corrugated surfaces. Geometrical dynamical equations are derived for the…
The scientific question resolved by this paper is that the continuity equation appears as an equivalent language of the system of first-order linear ODE. The main result characterizes the fact that the continuity equation contains…
We examine here various aspects of the statics and dynamics of disordered elastic systems such as manifolds and periodic systems. Although these objects look very similar and indeed share some underlying physics, periodic systems constitute…
The elastic energy of a planar convex body is defined by $E(\Om)=\frac 12\,\int\_{\partial\Om} k^2(s)\,ds$where $k(s)$ is the curvature of the boundary. In this paper we are interested in the minimization problemof $E(\Om)$ with a…
A switching dynamical system by means of piecewise linear systems in R^3 that presents multistability is presented. The flow of the system displays multiple scroll attractors due to the unstable hyperbolic focus-saddle equilibria with…
The three-dimensional elastic-plastic deformation is considered. The catastrophe theory underlies the construction of this process model. It was shown that the variety of stable states consists on elastic states and can be depicted as a…
In complex crystals close to melting or at finite temperatures, different types of defects are ubiquitous and their role becomes relevant in the mechanical response of these solids. Conventional elasticity theory fails to provide a…
For system of two ordinary differential equations of the second order representing autonomous non-conservative holonomic mechanical system, in case of dynamics such as one-frequency periodical oscillations, is found integrated invariant of…
The elastic flow, which is the $L^2$-gradient flow of the elastic energy, has several applications in geometry and elasticity theory. We present stable discretizations for the elastic flow in two-dimensional Riemannian manifolds that are…
New lattice model for the gradient elasticity is suggested. This lattice model gives a microstructural basis for second-order strain-gradient elasticity of continuum that is described by the linear elastic constitutive relation with the…
Stability is among the most important concepts in dynamical systems. Local stability is well-studied, whereas determining how "globally stable" a nonlinear system is very challenging. Over the last few decades, many different ideas have…
We extend the equations of motion that describe non-relativistic elastic collision of two particles in one dimension to an arbitrary associative algebra. Relativistic elastic collision equations turn out to be a particular case of these…
In the present article we determine the exact shape of an ideal spring suspended at both ends. Historically, this goes under the name of Elastica problem. The total energy of the suspended spring is a functional depending on two independent…
We study, both analytically and numerically, the dynamics of elastic boundaries such as crack fronts in fracture and surfaces of contact in solid on solid friction. The elastic waves in the solid give rise to kinks that move with a…