Related papers: Strings attached: New light on an old problem

In this study a new approach to the problem of transverse vibrations of an ideal string is presented. Unlike previous studies, assumptions such as constant tension, inextensibility, constant crosssectional area, small deformations and…

The dispute about the well-known 1D vibrating string model and its solutions, known as The Vibrating String Controversy, spanned the whole of 1700s and involved a group of the most eminent scientists of the time. After that, the model stood…

I study a relativistic open string coupling through its endpoints to a plane wave with arbitrary temporal profile. The string's transverse oscillations respond linearly to the external field. This makes it possible to solve the classical…

String vibration represents an active field of research in acoustics. Small-amplitude vibration is often assumed, leading to simplified physical models that can be simulated efficiently. However, the inclusion of nonlinear phenomena due to…

The vibrating string is a source of gravitational waves which requires novel computational techniques, based on the explicit construction of a conserved and renormalized (in a classical sense) energy-momentum tensor. The renormalization is…

The equations of motion governing small elastic oscillations of materials, induced by gravitational waves, are derived from the general framework of Carter and Quintana. In transverse-traceless gauge, no bulk forces are present, and the…

We study the perturbative dynamics of an infinite gravitating Nambu-Goto string within the general-relativistic perturbation framework. We develop the gauge invariant metric perturbation on a spacetime containing a self-gravitating straight…

We study the small vibrations of axially moving strings described by a wave equation in an interval with two endpoints moving in the same direction with a constant speed. The solution is expressed by a series formula where the coefficients…

In many introductory-level physics textbooks, the derivation of the formula for the speed of transverse waves in a string is either omitted altogether or presented under physically overly idealized assumptions about the shape of the…

This paper is concerned with the global stability of the plane wave solutions to the relativistic string equation with non-small perturbations. Under certain decay assumptions on the plane wave, we conclude that the perturbed system admits…

Conventional descriptions of transverse waves in an elastic solid are limited by an assumption of infinitesimally small gradients of rotation. By assuming a linear response to variations in orientation, we derive an exact description of a…

In classical mechanics, the motion of an object is described with Newton's three laws of motion, which means that the motion of the material elements composing a continuum can be described with the particle model. However, this viewpoint is…

The Conformal Field Theory of the current algebra of the centrally extended 2-d Euclidean group is analyzed. Its representations can be written in terms of four free fields (without background charge) with signature ($-$+++). We construct…

The hitherto controversial proposition that a ``wiggly" Goto-Nambu cosmic string can be effectively represented by an elastic string model of exactly transonic type (with energy density $U$ inversely proportional to its tension $T$) is…

In this work we obtain an approximate solution of the strongly nonlinear second order differential equation $\frac{d^{2}u}{dt^{2}}+\omega ^{2}u+\alpha u^{2}\frac{d^{2}u}{dt^{2}}+\alpha u\left( \frac{du}{dt}\right)^{2}+\beta \omega…

Here we are concerned about uniform stability of damped nonlinear transverse vibrations of an elastic string fixed at its two ends. The vibrations governed by nonlinear integro-differential equation of Kirchoff type, is shown to possess…

Navier equations are used to describe the deformation of a homogeneous, isotropic and linear elastic medium in the absence of body forces. Mathematically, the system is a natural vector (field) $O(n,\mbb{R})$-invariant generalization of the…

The full characterization of a stringed musical instrument requires measuring the motion of the strings in at least two dimensions. Traditionally this has been done using electromagnetic means or by optical transmission. However in many…

We measure and compare the rotational and transverse velocity of a bowed string. When bowed by an experienced player, the torsional motion is phase-locked to the transverse waves, producing highly periodic motion. The spectrum of the…

We study the immersed boundary problem in 2-D. It models a 1-D elastic closed string immersed and moving in a fluid that fills the entire plane, where the fluid motion is governed by the 2-D incompressible Navier-Stokes equation with a…