Related papers: A differentiable N-body code for transit timing an…
Optimization-based robot control strategies often rely on first-order dynamics approximation methods, as in iLQR. Using second-order approximations of the dynamics is expensive due to the costly second-order partial derivatives of the…
We consider an integro-differential equation model for traffic flow which is an extension of the Burgers equation model. To discuss the model, we first examine general settings for integrable integro-differential equations and find that…
Initial conditions for (Newtonian) cosmological N-body simulations are usually set by re-scaling the present-day power spectrum obtained from linear (relativistic) Boltzmann codes to the desired initial redshift of the simulation. This…
We present an efficient variational integrator for multibody systems. Variational integrators reformulate the equations of motion for multibody systems as discrete Euler-Lagrange (DEL) equations, transforming forward integration into a…
The study of multiple extrasolar planetary systems has the opportunity to obtain constraints for the planetary masses and orbital inclinations via the detection of mutual perturbations. The analysis of precise radial velocity measurements…
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…
A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic…
We describe a technique for solving for the orbital elements of multiple planets from radial velocity (RV) and/or astrometric data taken with 1 m/s and microarcsecond precision, appropriate for efforts to detect Earth-massed planets in…
We study analytically and experimentally certain symplectic and time-reversible N-body integrators which employ a Kepler solver for each pair-wise interaction, including the method of Hernandez & Bertschinger (2015). Owing to the Kepler…
The reproducibility of experiments is one of the main principles of the scientific method. However, numerical N-body experiments, especially those of planetary systems, are currently not reproducible. In the most optimistic scenario, they…
Symplectic integrators that preserve the geometric structure of Hamiltonian flows and do not exhibit secular growth in energy errors are suitable for the long-term integration of N-body Hamiltonian systems in the solar system. However, the…
Symplectic integration algorithms have become popular in recent years in long-term orbital integrations because these algorithms enforce certain conservation laws that are intrinsic to Hamiltonian systems. For problems with large variations…
Symplectic integration algorithms are well-suited for long-term integrations of Hamiltonian systems because they preserve the geometric structure of the Hamiltonian flow. However, this desirable property is generally lost when adaptive…
Modeling of collisionless galactic systems is based on the N-body model, which requires large computational resources due to the long-range nature of gravitational forces. The most common method for calculating gravity is the TreeCode…
(Abridged) We describe a new iterative approach for the realization of equilibrium N-body systems for given density distributions. Our method uses elements of Schwarzschild's technique and of the made-to-measure method, but is based on a…
We describe the newly written code GADGET which is suitable both for cosmological simulations of structure formation and for the simulation of interacting galaxies. GADGET evolves self-gravitating collisionless fluids with the traditional…
Digital quantum simulation of many-body dynamics relies on Trotterization to decompose the target time evolution into elementary quantum gates operating at a fixed equidistant time discretization. Recent advances have outlined protocols…
This paper focuses on the parallel implementation of a direct $N$-body method~(particle-particle algorithm) and the application of multiple GPUs for galactic dynamics simulations. Application of a hybrid OpenMP-CUDA technology is considered…
Large-scale cosmological simulations are an indispensable tool for modern cosmology. To enable model-space exploration, fast and accurate predictions are critical. In this paper, we show that the performance of such simulations can be…
The numerical solution of time-dependent radiative transfer problems is challenging, both, due to the high dimension as well as the anisotropic structure of the underlying integro-partial differential equation. In this paper we propose a…