Related papers: A differentiable N-body code for transit timing an…
On large-scales, comparable to the horizon, the observable clustering properties of galaxies are affected by various general relativistic effects. To calculate these effects one needs to consistently solve for the metric, densities and…
Derivatives of equations of motion(EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and…
In most books the Delaunay and Lagrange equations for the orbital elements are derived by the Hamilton-Jacobi method: one begins with the 2-body Hamilton equations, performs a canonical transformation to the orbital elements, and obtains…
This work proposes a novel variational approximation of partial differential equations on moving geometries determined by explicit boundary representations. The benefits of the proposed formulation are the ability to handle large…
We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the relativistic N-body problem in a separable two-body basis in which the particles interact pair-wise through scalar and vector interactions. The resultant N-body…
Modeling self-gravity of collisionless fluids (e.g. ensembles of dark matter, stars, black holes, dust, planetary bodies) in simulations is challenging and requires some force softening. It is often desirable to allow softenings to evolve…
We investigate the computational performance of various numerical methods for the integration of the equations of motion and the variational equations for some typical classical many-body models of condensed matter physics: the…
We use gauge-invariant cosmological perturbation theory to calculate the displacement field that sets the initial conditions for $N$-body simulations. Using first and second-order fully relativistic perturbation theory in the…
We present TES, a new n-body integration code for the accurate and rapid propagation of planetary systems in the presence of close encounters. TES builds upon the classic Encke method and integrates only the perturbations to Keplerian…
We describe source code level parallelization for the {\tt kira} direct gravitational $N$-body integrator, the workhorse of the {\tt starlab} production environment for simulating dense stellar systems. The parallelization strategy, called…
In the simulation of biological molecules, it is customary to impose constraints on the fastest degrees of freedom to increase the time step. The evaluation of the involved constraint forces must be performed in an efficient manner, for…
The parallel code NMAGIC is an implementation of a particle-based method to create made-to-measure models in agreement with observations of galaxies. It works by slowly correcting the particle weights of an evolving N-body system, until a…
In non-relativistic mechanics the center of mass of an isolated system is easily separated out from the relative variables. For a N-body system these latter are usually described by a set of Jacobi normal coordinates, based on the…
The large dynamic range in some astrophysical N-body problems led to the use of adaptive multi-time-steps; however, the search for optimal strategies is still challenging. We numerically quantify the performance of the hierarchical…
Numerical simulations of self-gravitating systems are generally based on N-body codes, which solve the equations of motion of a large number of interacting particles. This approach suffers from poor statistical sampling in regions of low…
A systolic algorithm rhythmically computes and passes data through a network of processors. We investigate the performance of systolic algorithms for implementing the gravitational N-body problem on distributed-memory computers. Systolic…
Most dynamic simulation tools parameterize the configuration of multi-body robotic systems using minimal coordinates, also called generalized or joint coordinates. However, maximal-coordinate approaches have several advantages over…
This paper proposes a task-specific trajectory optimization framework for human-robot collaboration, enabling adaptive motion planning based on human interaction dynamics. Unlike conventional approaches that rely on predefined desired…
We present a variational integrator based on the Lobatto quadrature for the time integration of dynamical systems issued from the least action principle. This numerical method uses a cubic interpolation of the states and the action is…
Upcoming Large Scale Structure surveys aim to achieve an unprecedented level of precision in measuring galaxy clustering. However, accurately modeling these statistics may require theoretical templates that go beyond second-order…