Related papers: Dynamical systems, celestial mechanics, and music:…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
In this paper, two models of interest for Celestial Mechanics are presented and analysed, using both analytic and numerical techniques, from the point of view of the possible presence of regular and/or chaotic motion, as well as the…
Most music theory books are like medieval medical textbooks: they contain unjustified superstition, non-reasoning, and funny symbols glorified by Latin phrases. How does music, in particular harmony, actually work, presented as a real,…
Building on earlier work, we discuss a general framework for exploring the cosmological dynamics of Higher Order Theories of Gravity. We show that once the theory of gravity has been specified, the cosmological equations can be written as a…
Strong dynamics constitutes one of the pillars of the standard model of particle interactions, and it accounts for the bulk of the visible matter in the universe. It is therefore a well posed question to ask if the rest of the universe can…
By a "scheme" of a musical canon, we mean the time and pitch displacement of each entering voice. When the time displacements are unequal, achieving consonant sonorities is especially challenging. Using a first-species theoretical model, we…
Despite the success of our best models in Theoretical Physics, especially concerning Cosmology and Particle Physics, we still face persistent challenges. Among them we have the cosmological singularity problem, understanding the late-time…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
This article surveys the burgeoning area at the intersection of dynamical systems theory and algorithms for NP-hard problems. Traditionally, computational complexity and the analysis of non-deterministic polynomial-time (NP)-hard problems…
There has been an everlasting discussion around the concept of form in music. This work is motivated by such debate by using a complex systems framework in which we study the form as an emergent property of rhythm. Such a framework…
This article presents a general description of dynamical systems using the language of enriched functors and enriched natural transformations. This framework is essential to establish the equivalence of three descriptions of dynamics -- a…
The relationship between musical material and physical phenomena has become a topic in the musicological literature over the last several decades, particularly concerning elements of the musical system itself, and constructions found in the…
Recently, the research community has been exploring fractional calculus to address problems related to cosmology; in this approach, the gravitational action integral is altered, leading to a modified Friedmann equation, then the resulting…
Galactic disks lie at the heart of many of the most pressing astrophysical puzzles. There are sophisticated kinetic theories that describe some aspects of galaxy disk dynamics, but extracting quantitative predictions from those theories has…
We start from a quantum computational principle suggested for string theory in a previous paper and discuss how it might lead to a dynamical principle implying the correct classical gravitational limit. Besides this, we briefly look at some…
We investigate correlations among pitches in several songs and pieces of piano music by mapping them to one-dimensional walks. Two kinds of correlations are studied, one is related to the real values of frequencies while they are treated…
We consider the possibility that classical dynamical systems display motion in their lowest energy state, forming a time analogue of crystalline spatial order. Challenges facing that idea are identified and overcome. We display arbitrary…
We study the long-term dynamics of a planetary system composed of a star and a planet. Both bodies are considered as extended, non-spherical, rotating objects. There are no assumptions made on the relative angles between the orbital angular…
Stellar systems - star clusters, galaxies, dark matter haloes, and so on - are ubiquitous characters in the evolutionary tale of our Universe. This tutorial article is an introduction to the collective dynamical evolution of the very large…
Active motion is a concept in complex systems theory and was successfully applied to various problems in nonlinear dynamics. Explicit studies for gravitational potentials were missing so far. We interpret the Friedmann equations with…