Related papers: Dynamical systems, celestial mechanics, and music:…
Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations…
There are theories which implement the idea that the constants of nature may be "time dependent." These introduce new fields representing "evolving constants," in addition to physical fields. We argue that dynamical matter coupling…
An update is given on the current status of solar and stellar dynamos. At present, it is still unclear why stellar cycle frequencies increase with rotation frequency in such a way that their ratio increases with stellar activity. The…
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
We propose a new dynamical system formalism for the analysis of f(R) cosmologies. The new approach eliminates the need for cumbersome inversions to close the dynamical system and allows the analysis of the phase space of f(R)-gravity models…
Kepler's laws of planetary motion are deduced from those of a harmonic oscillator following Arnold. Conversely, the circular orbits through the Earth's center suggested by Galilei are consistent with an $r^{-5}$ potential as found before by…
Astronomical solutions provide calculated orbital and rotational parameters of solar system bodies based on the dynamics and physics of the solar system. Application of astronomical solutions in the Earth sciences has revolutionized our…
Dynamical systems are a broad class of mathematical tools used to describe the evolution of physical and computational processes. Traditionally these processes model changing entities in a static world. Picture a ball rolling on an empty…
We study the cosmological dynamics of a class of symmetric teleparallel gravity theories known as ``newer general relativity'' using the methods of dynamical systems, restricted to the case of vacuum solutions with a spatially flat…
For the Poincare gauge theory of gravity we consider the dynamical scalar torsion mode in a cosmological context. We explore in particular the possibility of using dynamical torsion to explain the current state of the accelerating Universe.…
Computer simulation of the time evolution in a classical system is a standard numerical method, used in numerous scientific articles in Natural Science. Almost all the simulations are performed by discrete Molecular Dynamics (MD). The…
Algorithmic composition of music has a long history and with the development of powerful deep learning methods, there has recently been increased interest in exploring algorithms and models to create art. We explore the utility of state…
Modern physics is based on three major theories - general relativity, quantum field theory, and (quantum) thermodynamics. Classical acoustics in fluids is usually regarded and studied as a part of classical mechanics, more precisely fluid…
A new class of modified theories of gravity, consisting of the superposition of the metric Einstein-Hilbert Lagrangian with an $f(\cal R)$ term constructed \`{a} la Palatini was proposed recently. The dynamically equivalent scalar-tensor…
To understand the observational properties of cosmological models, in particular, the temperature of the cosmic microwave background radiation, it is necessary to study their null geodesics. Dynamical systems theory, in conjunction with the…
In hybrid classical-quantum theories, the dynamics of the classical system induce the classicality of the quantum system, meaning that such models do not necessarily require a measurement postulate to describe probabilistic measurement…
Observations of distorted discs have highlighted the ubiquity of warps in a variety of astrophysical contexts. This has been complemented by theoretical efforts to understand the dynamics of warp evolution. Despite significant efforts to…
Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…
We generalize the concept of geometrical resonance to perturbed sine-Gordon, Nonlinear Schrödinger and Complex Ginzburg-Landau equations. Using this theory we can control different dynamical patterns. For instance, we can stabilize…
The paper deals with a dynamical system analysis related to phantom cosmological model . Here gravity is coupled to phantom scalar field having scalar coupling function and a potential. The field equations are reduced to an autonomous…