Related papers: Some Static Properties of Slinky
In this paper, we introduce discrete conics, polygonal analogues of conics. We show that discrete conics satisfy a number of nice properties analogous to those of conics, and arise naturally from several constructions, including the…
The incessant swimming motion of microbes in dense suspensions can give rise to striking collective motions and coherent structures. However, theoretical investigations of these structures typically utilize either computationally demanding…
A new method has been proposed to evaluate the frictional force in the stationary state. This method is applied to the 1-dimensional model of clean surfaces. The kinetic frictional force is seen to depend on velocity in general, but the…
After surveying some known properties of compact convex sets in the plane, we give a two rigorous proofs of the general feeling that supporting lines can be slide-turned slowly and continuously. Targeting a wide readership, our treatment is…
In this paper, we are exploring some of the properties of the self-similar solutions of the first kind. In particular, we shall discuss the kinematic properties and also check the singularities of these solutions. We discuss these…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
We strengthen a result of two of us on the existence of effective interactions for discretised continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of…
In this paper we provide theoretical results that relate steady states of continuous and discrete models arising from biology.
Dense suspensions of particles are relevant to many applications and are a key platform for developing a fundamental physics of out-of-equilibrium systems. They present challenging flow properties, apparently turning from liquid to solid…
The dragging velocity of a model solid lubricant confined between sliding periodic substrates exhibits a phase transition between two regimes, respectively with quantized and with continuous lubricant center-of-mass velocity. The…
We investigate the sliding of objects on an inclined granular surface close to the avalanche threshold. Our experiments show that the stability is driven by the surface deformations. Heavy objects generate footprint-like deformations which…
It is shown on the basis of scaling arguments that a disordered interface between two elastic solids will quite generally exhibit static and "dry friction" (i.e., kinetic friction which does not vanish as the sliding velocity approaches…
This paper describes a lattice version of the Skyrme model in 2+1 and 3+1 dimensions. The discrete model is derived from a consistent discretization of the radial continuum problem. Subsequently, the existence and stability of the skyrmion…
We compile some easily deducible information on the discrete eigenvalue spectra of spinless Salpeter equations encompassing, besides a relativistic kinetic term, interactions which are expressible as superpositions of an attractive Coulomb…
We propose an elasto-plastic inspired friction model which incorporates interfacial stiffness. Steady state sliding friction is characterized by a generic nonmonotonic behavior, including both velocity weakening and strengthening branches.…
We examine some kinds of discrete symmetries which are dynamically preserved, using the (generalized) Gowdy models of the first kind.
A chain of interacting particles subject also to a nonlinear on-site potential admits stable soliton-like configurations : static kinks. The linear normal-modes around such a kink contain a discrete set of localized, gap-separated modes.…
In this paper we study the cyclicity of sliding cycles for regularized piecewise smooth visible-invisible two-folds, in the presence of singularities of the Filippov sliding vector field located away from two-folds. We obtain a slow-fast…
We study discrete solitons (kinks) accessible in state-of-the-art trapped ion experiments, considering zigzag crystals and quasi-3D configurations, both theoretically and experimentally. We first extend the theoretical understanding of…
Models which allow an explicit application to structurally modulated substances are reviewed within the frame of a symmetry-based approach starting from discrete lattice theory. Focus is set on models formulated in terms of local variables…