Related papers: A slow-down time-transformed symplectic integrator…
We present a new time integrator for articulated body dynamics. We formulate the governing equations of the dynamics using only the position variables and recast the position-based articulated dynamics as an optimization problem. Our…
An algebraic method has been developed which allows one to engineer several energy levels including the low-energy subspace of interacting spin systems. By introducing ancillary qubits, this approach allows k-body interactions to be…
The time step criterion plays a crucial role in direct N-body codes. If not chosen carefully, it will cause a secular drift in the energy error. Shared, adaptive time step criteria commonly adopt the minimum pairwise time step, which…
We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of…
A fixed time-step variational integrator cannot preserve momentum, energy, and symplectic form simultaneously for nonintegrable systems. This barrier can be overcome by treating time as a discrete dynamic variable and deriving adaptive…
We propose a new variational quantum algorithm, which we refer to as TIMES-ADAPT, that prepares time-evolved states in a low-energy or symmetric subspace of a time-independent Hamiltonian on a quantum computer. Using a specially trained…
Predicting the behaviors of Hamiltonian systems has been drawing increasing attention in scientific machine learning. However, the vast majority of the literature was focused on predicting separable Hamiltonian systems with their kinematic…
We present WHFast, a fast and accurate implementation of a Wisdom-Holman symplectic integrator for long-term orbit integrations of planetary systems. WHFast is significantly faster and conserves energy better than all other Wisdom-Holman…
The existence of explicit symplectic integrators for general nonseparable Hamiltonian systems is an open and important problem in both numerical analysis and computing in science and engineering, as explicit integrators are usually more…
We construct a symplectic integrator for non-separable Hamiltonian systems combining an extended phase space approach of Pihajoki and the symmetric projection method. The resulting method is semiexplicit in the sense that the main time…
The "gravitational million-body problem," to model the dynamical evolution of a self-gravitating, collisional N-body system with ~10^6 particles over many relaxation times, remains a major challenge in computational astrophysics.…
Simulations of the dynamics generated by partial differential equations (PDEs) provide approximate, numerical solutions to initial value problems. Such simulations are ubiquitous in scientific computing, but the correctness of the results…
Time-reversible symplectic methods, which are precisely compatible with Liouville's phase-volume-conservation theorem, are often recommended for computational simulations of Hamiltonian mechanics. Lack of energy drift is an apparent…
We present a new mixed variable symplectic (MVS) integrator for planetary systems, that fully resolve close encounters. The method is based on a time regularisation that allows keeping the stability properties of the symplectic integrators,…
Many important physical systems can be described as the evolution of a Hamiltonian system, which has the important property of being conservative, that is, energy is conserved throughout the evolution. Physics Informed Neural Networks and…
Symplectic methods, in particular the Wisdom-Holman map, have revolutionized our ability to model the long-term, conservative dynamics of planetary systems. However, many astrophysically important effects are dissipative. The consequences…
In early Solar System numerical simulations, where chaos is a primary driver, it is difficult to explore parameter space in a systematic way. In such simulations, stable configurations are hard to come by, and often require special…
Modeling interacting galaxies to reproduce observed systems is still a challenge due to the extended parameter space (among other problems). Orbit and basic galaxy parameters can be tackled by fast simulation techniques like the restricted…
Most numerical integration algorithms are not designed specifically for Hamiltonian systems and do not respect their characteristic properties, which include the preservation of phase space volume with time. This can lead to spurious…
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…