Related papers: Hybrid Symplectic Integrators for Planetary Dynami…
We propose a new explicit pseudo-energy and momentum conserving scheme for the time integration of Hamiltonian systems. The scheme, which is formally second-order accurate, is based on two key ideas: the integration during the time-steps of…
An improved understanding of Field Reversed Configuration (FRC) merging and stability in high acceleration and compression magnetic fields is needed to speed up the development of the pulsed fusion concept developed at Helion Energy. All…
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…
Calculating the long term solution of ordinary differential equations, such as those of the $N$-body problem, is central to understanding a wide range of dynamics in astrophysics, from galaxy formation to planetary chaos. Because generally…
The effective Hamiltonian method is a powerful tool for simulating large-scale systems across a wide range of temperatures. However, previous methods for constructing effective Hamiltonian models suffer from key limitations: some require to…
We provide new existence and uniqueness results for the discrete-time Hamilton (DTH) equations of a symplectic-energy-momentum (SEM) integrator. In particular, we identify points in extended-phase space where the DTH equations of SEM…
This paper addresses the problem of efficiently computing higher-order variational integrators in simulation and trajectory optimization of mechanical systems as those often found in robotic applications. We develop $O(n)$ algorithms to…
Identifying the underlying dynamics of physical systems can be challenging when only provided with observational data. In this work, we consider systems that can be modelled as first-order ordinary differential equations. By assuming a…
We investigate the effectiveness of tuning HMC parameters using information from the gradients of the HMC acceptance probability with respect to the parameters. In particular, the optimization of the trajectory length and parameters for…
The new method based on the SUSY algebra with supercharges of higher order in derivatives is proposed to search for dynamical symmetry operators in 2-dim quantum and classical systems. These symmetry operators arise when closing the SUSY…
A new family of methods involving complex coefficients for the numerical integration of differential equations is presented and analyzed. They are constructed as linear combinations of symmetric-conjugate compositions obtained from a basic…
To identify under what conditions guiding-centre or full-orbit tracing should be used, an estimation of the spatial variation of the magnetic field is proposed, not only taking into account gradient and curvature terms but also parallel…
We present new almost time-reversible integrators for solution of planetary systems consisting of "planets" and a dominant mass ("star"). The algorithms can be considered adaptive generalizations of the Wisdom--Holman method, in which all…
We construct explicit integrators of arbitrary even orders of accuracy for massive point vortex dynamics in binary mixture of Bose--Einstein condensates proposed by Richaud et al. The integrators are symplectic and preserve the angular…
As robotic systems increasingly operate in unstructured, cluttered, and previously unseen environments, there is a growing need for manipulators that combine compliance, adaptability, and precise control. This work presents a real-time…
Hamiltonian Monte Carlo is a prominent Markov Chain Monte Carlo algorithm, which employs symplectic integrators to sample from high dimensional target distributions in many applications, such as statistical mechanics, Bayesian statistics…
In recent work, we initiated a research program aimed at the systematic investigation of quantum superintegrable systems describing the interaction of two non-relativistic spin-$1/2$ particles in three-dimensional Euclidean space. In that…
Machine learning and deep learning have revolutionized computational physics, particularly the simulation of complex systems. Equivariance is essential for simulating physical systems because it imposes a strong inductive bias on the…
Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate…
Quantum Monte Carlo method with operator-loop update is a powerful technique that has been extensively used with great success in condensed matter physics. It enables one to sample from thermal and ground states of local Hamiltonians of…