Related papers: The Lamb Problem with a Nonuniform String
Synchronisation and stability under periodic oscillatory driving are well-understood, but little is known about the effects of aperiodic driving, despite its abundance in nature. Here, we consider oscillators subject to driving with slowly…
We discuss the extension of the Lewis and Riesenfeld method of solving the time-dependent Schr\"odinger equation to cases where the invariant has continuous eigenvalues and apply it to the case of a generalized time-dependent inverted…
Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…
We study analytically and numerically the problem of a nonlinear mechanical oscillator with additive noise in the absence of damping. We show that the amplitude, the velocity and the energy of the oscillator grow algebraically with time.…
We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise…
We consider string theory in a time dependent orbifold with a null singularity. The singularity separates a contracting universe from an expanding universe, thus constituting a big crunch followed by a big bang. We quantize the theory both…
Motivated by recent problems in mathematical cosmology, in which temporal averaging methods are applied in order to analyze the future asymptotics of models which exhibit oscillatory behavior, we provide a theorem concerning the large-time…
A perturbation theory with respect to tension parameter $\gamma/\alpha^\prime$ for the non--linear equations of string, moving in curved space--time is considered. Obtained are linearized motion equations for the functions of the $n-$th…
We investigate the time-periodic solutions to the nonlinear wave and beam equations and uncover their intricate, fractal-like structure. In particular, we identify a new class of large-energy solutions with complex mode compositions and…
Inspired by the cuprate stripes, the problem of a one dimensional metal living on a delocalized trajectory in two dimensional space is considered. Under the assumption that a localized and charge incompressible reference string state…
We study the system of equations of motion for inextensible strings. This system possesses many internal symmetries, and is related to discontinuous systems of conservation laws and the total variation wave equation. We prove existence of…
In this note we address the exact solutions of a time-dependent Hamiltonian composed by an oscillator-like interaction with both a frequency and a mass term that depend on time. The latter is achieved by constructing the appropriate point…
Under periodic boundary conditions, a one-dimensional dispersive medium driven by a Lamb oscillator exhibits a smooth response when the dispersion relation is asymptotically linear or superlinear at large wave numbers, but unusual fractal…
The time evolution of a Gaussian density matrix of a one dimensional particle, generated by a quadratic, ${\cal O}(\partial_t^2)$ effective Lagrangian, describing a harmonic potential, a friction force and decoherence, is studied within the…
A recent investigation shows that a local gauge string with a phenomenological energy momentum tensor, as prescribed by Vilenkin, is inconsistent in Brans-Dicke theory. In this work, it has been shown that such a string is indeed consistent…
A modification of the spiked harmonic oscillator is studied in the case for which the perturbation potential contains both an inverse power and a linear term. It is then possible to evaluate trial functions by solving an integral equation…
In this paper we analyze a Rutherford type experiment where light probes are inelastically scattered by an ensemble of excited closed strings, and use the corresponding cross section to extract density-density correlators between different…
We consider a one dimensional infinite chain of har- monic oscillators whose dynamics is perturbed by a stochastic term conserving energy and momentum. We prove that in the unpinned case the macroscopic evolution of the energy converges to…
In this paper we address the problem of consistently construct Langevin equations to describe fluctuations in non-linear systems. Detailed balance severely restricts the choice of the random force, but we prove that this property together…
The steady state motion of a folded pendulum has been studied using frequencies of drive that are mainly below the natural (resonance) frequency of the instrument. Although the free-decay of this mechanical oscillator appears textbook…