Related papers: On the probabilistic approach to the N-body proble…
In the last decades cosmological N-body dark matter simulations have enabled ab initio studies of the formation of structure in the Universe. Gravity amplified small density fluctuations generated shortly after the Big Bang, leading to the…
In this paper, we are interested in a generalised Vlasov equation, which describes the evolution of the probability density of a particle evolving according to a generalised Vlasov dynamic. The achievement of the paper is twofold. Firstly,…
We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that $n$ particles move forward on the real…
A recently proposed statistical theory of the mean fields associated with the ground and excited collective states of a generic many-body system is extended by increasing the dimensions of the P-space. In applying the new framework to…
We investigate the old problem of the fast relaxation of collisionless $N$-body systems which are collapsing or perturbed, emphasizing the importance of (non-collisional) discreteness effects. We integrate orbit ensembles in fixed external…
Suppose that an infinite lattice gas of constant density $n_0$, whose dynamics are described by the symmetric simple exclusion process, is brought in contact with a spherical absorber of radius $R$. Employing the macroscopic fluctuation…
We have two basic methods of modeling matter. We can treat matter as a continuum and solve differential equations or we can treat it discretely and solve massive N-body problems. The differential equations produced by meaningful problems…
I consider a self-gravitating, N-body system assuming that the N constituents follow regular orbits about the center of mass of the cluster, where a central massive object may be present. I calculate the average over a characteristic…
A simultaneous description of the dynamics of multiple particles requires a configuration space approach with an external time parameter. This is in stark contrast with the relativistic paradigm, where time is but a coordinate chosen by an…
This paper considers the problem of computing Bayesian estimates of both states and model parameters for nonlinear state-space models. Generally, this problem does not have a tractable solution and approximations must be utilised. In this…
A new and very general technique for simulating solid-fluid suspensions is described; its most important feature is that the computational cost scales linearly with the number of particles. The method combines Newtonian dynamics of the…
N-Body simulations are an important tool in the study of formation of large scale structures. Much of the progress in understanding the physics of galaxy clustering and comparison with observations would not have been possible without…
Future large-scale structure surveys of the Universe will aim to constrain the cosmological model and the true nature of dark energy with unprecedented accuracy. In order for these surveys to achieve their designed goals, they will require…
Reconstructing the Gaussian initial conditions at the beginning of the Universe from the survey data in a forward modeling framework is a major challenge in cosmology. This requires solving a high dimensional inverse problem with an…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
We study the bar instability in collisionless, rotating, anisotropic, stellar systems, using N-body simulations and also the matrix technique for calculation of modes with the perturbed collisionless Boltzmann equation. These methods are…
In this paper I focus on three topics related to the dynamical evolution of small galaxy groups, for which the input of N-body simulations has been decisive. These are the merging rates in compact groups, the properties of remnants of…
While accurate simulations of dense gas flows far from the equilibrium can be achieved by Direct Simulation adapted to the Enskog equation, the significant computational demand required for collisions appears as a major constraint. In order…
A formalism is presented for analytically obtaining the probability density function, (P_{n}(s)), for the random distance (s) between two random points in an (n)-dimensional spherical object of radius (R). Our formalism allows (P_{n}(s)) to…
The role of gravity is crucial in astrophysics. It determines the evolution of any system, over an enormous range of time and space scales. Astronomical stellar systems as composed by N interacting bodies represent examples of…