Related papers: The 4-Body Problem in a (1+1)-Dimensional Self-Gra…
A Lyapunov-based approach for the trajectory generation of an $N$-dimensional Schr{\"o}dinger equation in whole $\RR^N$ is proposed. For the case of a quantum particle in an $N$-dimensional decaying potential the convergence is precisely…
This work provides an experimental method for simultaneously measuring finite time Lyapunov exponent fields for multiple particle groups, including non-flow tracers, in three-dimensional multiphase flows. From sequences of particle images,…
A non-linear relativistic 4D field model of a quantum particle which emerges from the internal dynamics in the quantum phase space $CP(N-1)$ is proposed. In this model there is no distinction between `particle' and its `surrounding field',…
The geometry of 4D simplicial quantum gravity with a U(1) gauge field is studied numerically. The phase diagram shows a continuous transition when gravity is coupled with a U(1) gauge field. At the critical point measurements of the…
Using geometric mechanics methods, we examine aspects of the dynamics of n mass points in $\mathbb{R}^4$ with a general pairwise potential. We investigate the central force problem, set up the n-body problem and discuss certain properties…
The plane case of central configurations with four different masses is analyzed theoretically and is computed numerically. We follow Dziobek's approach to four body central configurations with a direct implicit method of our own in which…
We investigate regular and chaotic dynamics of Two Bodies Swinging on a Rod, which differs from all the other mechanical analogies: depending on initial conditions, its oscillation could end very quickly and the reason is not a drag force…
We consider a system of gravitating bodies in Kaluza-Klein models with toroidal compactification of extra dimensions. To simulate the astrophysical objects (e.g., our Sun and pulsars) with the energy density much greater than the pressure,…
We study the stability of a family of spherical equilibrium models of self-gravitating systems, the so-called $\gamma-$models with Osipkov-Merritt velocity anisotropy, by means of $N-$body simulations. In particular, we analyze the effect…
Dynamics of regular clusters of many non-touching particles falling under gravity in a viscous fluid at low Reynolds number are analysed within the point-particle model. Evolution of two families of particle configurations is determined: 2…
We present a fully covariant transport framework for Molecular Dynamics that enables a consistent description of the evolution of relativistic N-body systems. For the first time, we derive relativistic equations of motion incorporating both…
The four-body bound state with two-body forces is formulated by the Three-Dimensional approach, which greatly simplifies the numerical calculations of few-body systems without performing the Partial Wave components. We have obtained the…
We consider one-dimensional systems of self-gravitating sticky particles with random initial data and describe the process of aggregation in terms of the largest cluster size L_n at any fixed time prior to the critical time. The asymptotic…
We have investigated the appearance of chaos in the 1-dimensional Newtonian gravitational three-body system (three masses on a line with $-1/r$ pairwise potential). We have concentrated in particular on how the behavior changes when the…
A description of many-particle systems, which is more fundamental than the fluid approach, is to consider them as a kinetic gas. In this approach the dynamical variable in which the properties of the system are encoded, is the distribution…
We summarise the recent theoretical progress in few-body descriptions of the piNN system. Previous descriptions, both three- and four-dimensional, are shown to possess serious theoretical inconsistencies. We illustrate how three-dimensional…
We propose the model of massive spinning particle traveling in four-dimensional Minkowski space. The equations of motion of the particle follow from the fact that all the classical paths of the particle lie on a cylinder whose position in…
Gravitational instability is a key process that may lead to fragmentation of gaseous structures (sheets, filaments, haloes) in astrophysics and cosmology. We introduce here a method to derive analytic expressions for the growth rate of…
The use in the action integral of a volume element of the form $\Phi d^{D}x$ where $\Phi$ is a metric independent measure can give new interesting results in all types of known generally coordinate invariant theories: (1) 4-D theories of…
We study the influence of the dimension of space on the thermodynamics of the classical and quantum self-gravitating gas. We consider Hamiltonian systems of self-gravitating particles described by the microcanonical ensemble and…