Related papers: Hybrid Symplectic Integrators for Planetary Dynami…
Polynomial approximations to the inverse of the fermion matrix are used to filter the dynamics of the upper energy scales in HMC simulations. The use of a multiple time-scale integration scheme allows the filtered pseudofermions to be…
We present a multiscale integrator for Hamiltonian systems with slowly varying quadratic stiff potentials that uses coarse timesteps (analogous to what the impulse method uses for constant quadratic stiff potentials). This method is based…
In recent years, much effort in designing numerical methods for the simulation and optimization of mechanical systems has been put into schemes which are structure preserving. One particular class are variational integrators which are…
To distinguish between regular and chaotic orbits in Hamiltonian systems, the Global Symplectic Integrator (GSI) has been introduced, based on the symplectic integration of both Hamiltonian equations of motion and variational equations. In…
We present a new approach to simulating Hamiltonian dynamics based on implementing linear combinations of unitary operations rather than products of unitary operations. The resulting algorithm has superior performance to existing simulation…
We explore the construction of new symplectic numerical integration schemes to be used in Hamiltonian Monte Carlo and study their efficiency. Two integration schemes from Blanes et al. (2014), and a new scheme based on optimal acceptance…
We describe a technique for constructing a symplectic transfer map for a charged particle moving through an accelerator component with arbitrary three-dimensional static magnetic field. The transfer map is constructed by symplectic…
In this paper we study the performance of a symplectic numerical integrator based on the splitting method. This method is applied to a subtle problem i.e. higher order resonance of the elastic pendulum. In order to numerically study the…
Modular robotics holds immense potential for space exploration, where reliability, repairability, and reusability are critical for cost-effective missions. Coordination between heterogeneous units is paramount for precision tasks -- whether…
We implement and investigate the numerical properties of a new family of integrators connecting both variants of the symplectic Euler schemes, and including an alternative to the classical symplectic mid-point scheme, with some additional…
Hybrid Monte Carlo simulations that implement the fermion action using multiple terms are commonly used. By the nature of their formulation they involve multiple integration time scales in the evolution of the system through simulation…
The Hybrid Monte Carlo (HMC) algorithm currently is the favorite scheme to simulate quantum chromodynamics including dynamical fermions. In this talk-which is intended for a non-expert audience--I want to bring together methodical and…
We examine a new 2nd order integrator recently found by Omelyan et al. The integration error of the new integrator measured in the root mean square of the energy difference, $\bra\Delta H^2\ket^{1/2}$, is about 10 times smaller than that of…
Hamiltonian systems are known to conserve the Hamiltonian function, which describes the energy evolution over time. Obtaining a numerical spatio-temporal scheme that accurately preserves the discretized Hamiltonian function is often a…
Optimally selecting a subset of targets from a larger catalog is a common problem in astronomy and cosmology. A specific example is the selection of targets from an imaging survey for multi-object spectrographic follow-up. We present a new…
We construct integrators to be used in Hamiltonian (or Hybrid) Monte Carlo sampling. The new integrators are easily implementable and, for a given computational budget, may deliver five times as many accepted proposals as standard…
Symplectic numerical methods have become a widely-used choice for the accurate simulation of Hamiltonian systems in various fields, including celestial mechanics, molecular dynamics and robotics. Even though their characteristics are…
Due to the chaotic nature of the Solar System, the question of its long-term stability can only be answered in a statistical sense, for instance, based on numerical ensemble integrations of nearby orbits. Destabilization of the inner…
Heliospheric plasmas require multi-scale and multi-physics considerations. On one hand, MHD codes are widely used for global simulations of the solar-terrestrial environments, but do not provide the most elaborate physical description of…
Efficient performance of a number of engineering systems is achieved through different modes of operation - yielding systems described as "hybrid", containing both real-valued and discrete decision variables. Prominent examples of such…