Related papers: An optimum time-stepping scheme for N-body simulat…
An algorithm for planning near time-optimal trajectories for systems with an oscillatory internal dynamics has been developed in previous work. It is based on assembling a complete trajectory from motion primitives called jerk segments,…
For the classical N-body problem, an approach is proposed based on the introduction of some natural in the physical sense optimization problems of mathematical programming for finding a conditional minimum for the characteristics of the…
For problems in astrophysics, planetary science and beyond, numerical simulations are often limited to simulating fewer particles than in the real system. To model collisions, the simulated particles (aka superparticles) need to be inflated…
Quantum particle simulations have largely been based on time-independent, split-operator schemes in which kinetic and potential operators are interwoven to provide accurate approximations to system dynamics. These simulations can be very…
We simultaneously study the dynamics of the growth of errors and the question of the faithfulness of simulations of $N$-body systems. The errors are quantified through the numerical reversibility of small-$N$ spherical systems, and by…
In this note we approach the classical, Newtonian, gravitational $N$-body problem by mean of a new, original numerical integration method. After a short summary of the fundamental characteristics of the problem, including a sketch of some…
Using cosmological N-body simulations we study the line-of-sight velocity distribution of dark matter haloes focusing on the lowest-order even moments, dispersion and kurtosis, and their application to estimate the mass profiles of…
We present a methodology for simulating dilute suspensions of particles settling under gravity, with the main purpose of overcoming limitations of triply periodic configurations, mainly the strong vertical correlation that hinders the study…
Run-and-tumble particles constitute one of the simplest models of self-propelled active matter, and provide an ideal playground to the understanding of out-of-equilibrium systems. We consider an idealized setup where one such particle is…
Based on the particle-in-cell (PIC) plasma simulation method, the speed-limited PIC (SLPIC) method delivers faster kinetic plasma simulation in cases where the particle distributions evolve slowly compared with the maximum stable PIC…
Inaccuracies in the initial conditions for cosmological N-body simulations could easily be the largest source of systematic error in predicting the non-linear large-scale structure. From the theory side, initial conditions are usually…
Collisions are common in many dynamical systems with real applications. They can be formulated as hybrid dynamical systems with discontinuities automatically triggered when states transverse certain manifolds. We present an algorithm for…
A new approach for integration of motion in many-body systems of interacting polyatomic molecules is proposed. It is based on splitting time propagation of pseudo-variables in a modified phase space, while the real translational and…
We describe efforts over the last six years to implement regularization methods suitable for studying one or more interacting black holes by direct N-body simulations. Three different methods have been adapted to large-N systems: (i)…
We present a novel $N$-body simulation method that compactifies the infinite spatial extent of the Universe into a finite sphere with isotropic boundary conditions to follow the evolution of the large-scale structure. Our approach…
We introduce a class of fourth order symplectic algorithms that are ideal for doing long time integration of gravitational few-body problems. These algorithms have only positive time steps, but require computing the force gradient in…
For the well-known model of a system of N particles with interaction (N-body problem), we consider the spatial problem of finding the minimum of the function of the kinetic energy of a system on its phase space under conditions on its size…
The discovery of interstellar interlopers such as 1I/`Oumuamua, 2I/Borisov, and 3I/ATLAS have highlighted the necessity of understanding the dynamical pathways that eject small bodies from planetary systems into hyperbolic trajectories. In…
Computational chemistry allows researchers to experiment in sillico: by running a computer simulations of a biological or chemical processes of interest. Molecular dynamics with molecular mechanics model of interactions simulates N-body…
We present a novel reformulation of nonsmooth differential equations with state jumps which enables their easier simulation and use in optimal control problems without the need of using integer variables. The main idea is to introduce an…