Related papers: Dynamical systems, celestial mechanics, and music:…
The theory of the dynamical systems is a very complex subject which has brought several surprises in the recent past in connection with the theory of chaos and fractals. The application of the tools of the dynamical systems in cosmological…
We discuss the principles to be used in the construction of discrete time classical and quantum mechanics as applied to point particle systems. In the classical theory this includes the concept of virtual path and the construction of system…
Scattered disk objects (SDOs) are distant minor bodies that orbit the sun on highly eccentric orbits, frequently with perhelia near Neptune's orbit. Gravitational perturbations due to Neptune frequently lead to chaotic dynamics, with the…
Modal synthesis methods are a long-standing approach for modelling distributed musical systems. In some cases extensions are possible in order to handle geometric nonlinearities. One such case is the high-amplitude vibration of a string,…
After presenting the general framework of 'mathemusical' dynamics, we focus on one music-theoretical problem concerning a special case of homometry theory applied to music composition, namely Milton Babbitt's hexachordal theorem. We briefly…
The Pythagorean school attributed consonance in music to simplicity of frequency ratios between musical tones. In the last two centuries, the consonance curves developed by Helmholtz, Plompt and Levelt shifted focus to psycho-acoustic…
Classical, self-consistent theory of statistical mechanics was developed for the thermodynamic and conservative Hamiltonian systems. Later there were many attempts (Sinai-Bowen-Ruelle's temperature, Tsallis' non-extensive theory) to apply…
Deterministic chaos, and even maximum computational complexity, have been discovered within Newtonian dynamics. Economists assume that prices and price changes can also obey abstract mathematical laws of motion. Sociologists and other…
Many interesting physical systems have mathematical descriptions as finite-dimensional or infinite-dimensional Hamiltonian systems. Poincare who started the modern theory of dynamical systems and symplectic geometry developed a particular…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
We investigate cosmological dynamics based on $f(R)$ gravity in the Palatini formulation. In this study we use the dynamical system methods. We show that the evolution of the Friedmann equation reduces to the form of the piece-wise smooth…
The nervous system displays a variety of rhythms in both waking and sleep. These rhythms have been closely associated with different behavioral and cognitive states, but it is still unknown how the nervous system makes use of these rhythms…
The mechanism of irreversible dynamics in the systems with mixing is analyzed. The procedure of splitting of system on equilibrium subsystems and studying of dynamics of one of them under condition of its interaction with other subsystems…
It is common for most people to think of science and art as disparate, or at most only vaguely related fields. In physics, one of the biggest successes of thermodynamics is its explanation of order arising from disordered phases of matter…
Temporal logics are an obvious high-level descriptive companion formalism to dynamical systems which model behavior as deterministic evolution of state over time. A wide variety of distinct temporal logics applicable to dynamical systems…
Towards the end of nineteenth century, Celestial Mechanics provided the most powerful tools to test Newtonian gravity in the solar system, and led also to the discovery of chaos in modern science. Nowadays, in light of general relativity,…
In this work we show a technique that allows for the musical interpretation of the brightness variations of stars. This method allows composers a lot of freedom to incorporate their own ideas into the score, based on the melodic line…
We apply results from nonlinear dynamics to an old problem in acoustical physics: the mechanism of the perception of the pitch of sounds, especially the sounds known as complex tones that are important for music and speech intelligibility.
We discuss the dynamical system approach applied to Higher Order Theories of Gravity. We show that once the theory of gravity has been specified, the cosmological equations can be written as a first-order autonomous system and we give…
In classical music and in any genre of contemporary music, the tonal elements or notes used for playing are the same. The numerous possibilities of chords for a given instance in a piece make the playing, in general, very intricate, and…