Related papers: The Lamb Problem with a Nonuniform String

We consider the response of a finite string to white noise and obtain the exact time-dependent spectrum. The complete exact solution is obtained, that is, both the transient and steady-state solution. To define the time-varying spectrum we…

We explore via linearized perturbation theory the Gregory-Laflamme instability of rotating black strings with equal magnitude angular momenta. Our results indicate that the Gregory-Laflamme instability persists up to extremality for all…

In this paper we study the stability of an homogeneous black string in the presence of a negative cosmological constant with minimally coupled scalar fields by using the large $D$ effective theory. This method allows us to explore the…

We attempt to understand the fate of spacelike gravitational singularities in string theory via the quantum stress tensor for string matter in a fixed background. We first approximate the singularity with a homogeneous anisotropic…

This paper considers the stability problem of a linear time invariant system in feedback with a string equation. A new Lyapunov functional candidate is proposed based on the use of augmented states which enriches and encompasses the…

We study the long time behaviour of a nonlinear oscillator subject to a random multiplicative noise with a spectral density (or power-spectrum) that decays as a power law at high frequencies. When the dissipation is negligible, physical…

This paper discusses aspects of the second order hyperbolic partial differential equation associated with the ideal lossless string under tension and it's relationship to two discrete models. These models are finite differencing in the time…

We show that the natural resonant frequency of a suspended flexible string is significantly modified (by one order of magnitude) by adding a freely pivoting attached mass at its lower end. This articulated system then exhibits complex…

We study a 1D semilinear wave equation modeling the dynamic of an elastic string interacting with a rigid substrate through an adhesive layer. The constitutive law of the adhesive material is assumed elastic up to a finite critical state,…

We study the unitary time evolution of the entropy of entanglement of a one-dimensional system between the degrees of freedom in an interval of length l and its complement, starting from a pure state which is not an eigenstate of the…

A noisy damping parameter in the equation of motion of a nonlinear oscillator renders the fixed point of the system unstable when the amplitude of the noise is sufficiently large. However, the stability diagram of the system can not be…

We investigate energy transfer and localization in a linear time-invariant oscillator chain weakly coupled to a forced nonlinear actuator. Two types of perturbation are studied: (1) harmonic forcing with a constant frequency is applied to…

We subject the stationary solutions of inviscid and axially symmetric rotational accretion to a time-dependent radial perturbation, which includes nonlinearity to any arbitrary order. Regardless of the order of nonlinearity, the equation of…

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…

We consider non-stationary free and forced transverse oscillation of an infinite taut string on the Winkler foundation subjected to a discrete mass-spring system non-uniformly moving at a given sub-critical speed. The speed of the…

In this paper we review the recent progress in the (indefinite) string density problem and its applications to the Camassa--Holm equation.

We analyze a simple example of wave equation with a time-dependent damping term, whose coefficient decays at infinity at the scale-invariant rate and includes an oscillatory component that is integrable but not absolutely integrable. We…

An infinite irregular harmonic chain of particles is considered. We assume that some particles (``defects'') in the chain have masses and force constants of interaction different from the masses and the interaction constants of the other…

The dynamics of models described by a one-dimensional discrete nonlinear Schr\"odinger equation is studied. The nonlinearity in these models appears due to the coupling of the electronic motion to optical oscillators which are treated in…

We obtain systematic approximations for the modes of vibration of a string of variable density, which is held fixed at its ends. These approximations are obtained iteratively applying three theorems which are proved in the paper and which…