Related papers: The wave equation for stiff strings and piano tuni…
Following the ideas of von Helmholtz and Plomp-Levelt, an algorithm for calculating the total dissonance of complex sounds, free from logical inconsistencies and useful for comparing different chords, is proposed. The method is tested by…
We report on the geometry and mechanics of knotted stiff strings. We discuss both closed and open knots. Our two main results are: (i) Their equilibrium energy as well as the equilibrium tension for open knots depend on the type of knot as…
The variational perturbation theory for wave functions, which has been shown to work well for bound states of the anharmonic oscillator, is applied to resonance states of the anharmonic oscillator with negative coupling constant. We obtain…
We consider the simplest instabilities involving multiple unstable electrostatic plasma waves corresponding to four-dimensional systems of mode amplitude equations. In each case the coupled amplitude equations are derived up to third order…
We consider the sharp Strichartz estimate for the wave equation on $\mathbb R^{1+5}$ in the energy space, due to Bez and Rogers. We show that it can be refined by adding a term proportional to the distance from the set of maximisers, in the…
For a one-dimensional wave equation, we consider a mixed problem in a curvilinear half-strip. The initial conditions have a first-kind discontinuity at one point. The mixed problem models the problem of a longitudinal impact on a finite…
A theory for obtaining waveform for the effective entrainment of a weakly forced oscillator is presented. Phase model analysis is combined with calculus of variation to derive a waveform with which entrainment of an oscillator is achieved…
Thin enough black strings are unstable to growing ripples along their length, eventually pinching and forming a naked singularity on the horizon. We investigate how string theory can resolve this singularity. First, we study the…
Variety of statistically steady energy spectra in elastic wave turbulence have been reported in numerical simulations, experiments, and theoretical studies. Focusing on the energy levels of the system, we have performed direct numerical…
We analyse two issues that arise in the context of (matrix) string theories in plane wave backgrounds, namely (1) the use of Brinkmann- versus Rosen-variables in the quantum theory for general plane waves (which we settle conclusively in…
We consider the inverse problem for the wave equation which consists of determining an unknown space-dependent force function acting on a vibrating structure from Cauchy boundary data. Since only boundary data are used as measurements, the…
An axisymmetric static solution of a nonlinear electrodynamics is considered as a massive charged particle with spin and magnetic moment. A linearization of the nonlinear electrodynamics around the static solution is investigated. The…
The intensity of an electromagnetic wave interacting self-consistently with a beam of charged particles as in a free electron laser, displays large oscillations due to an aggregate of particles, called the macro-particle. In this article,…
Why are white and black piano keys in an octave arranged as they are today? This article examines the relations between abstract algebra and key signature, scales, degrees, and keyboard configurations in general equal-temperament systems.…
The wolf note is an acoustic instability that occurs in large bowed string instruments when a strong body resonance interacts with the vibrating string, producing amplitude modulation and loss of tonal control. Various wolf suppressors -…
An ill-posed Cauchy problem for the wave equation is considered: the solution is to be determined by the Cauchy data on some part of the time-space boundary. By means of Fourier method we obtain a regularization algorithm for this problem,…
Audio-to-score alignment is a long-standing challenge in music information retrieval and arguably the most widely applicable alignment task for music research. Alignment algorithms match two versions of a piece of music, and for this to…
Even if the tuning between the first and second register of a clarinet has been optimized by instrument makers, the lowest twelfths remain slightly too large (inharmonicity). In this article, we study the problem from two different points…
We propose an accurate numerical scheme for approximating the solution of the two dimensional acoustic wave problem. We use machine learning to find a stencil suitable even in the presence of high wavenumbers. The proposed scheme…
After briefly revising the concepts of consonance/dissonance, a respective mathematic-computational model is described, based on Helmholtz's consonance theory and also considering the partials intensity. It is then applied to characterize…