Related papers: Symplectic tracking through curved three dimension…
We describe the symplectic structure and Hamiltonian dynamics for a class of Grassmannian manifolds. Using the two dimensional sphere ($S^2$) and disc ($D^2$) as illustrative cases, we write their path integral representations using…
In a previous paper, second- and fourth-order explicit symplectic integrators were designed for a Hamiltonian of the Schwarzschild black hole. Following this work, we continue to trace the possibility of the construction of explicit…
We introduce symplectic quantization, a novel functional approach to quantum field theory which allows to sample quantum fields fluctuations directly in Minkowski space-time, at variance with the traditional importance sampling protocols,…
The symplectic Wisdom-Holman map revolutionized long-term integrations of planetary systems. There is freedom in such methods of how to split the Hamiltonian and which coordinate system to employ, and several options have been proposed in…
This paper studies explicit symplectic adapted exponential integrators for solving charged-particle dynamics in a strong and constant magnetic field. We first formulate the scheme of adapted exponential integrators and then derive its…
In previous papers, explicit symplectic integrators were designed for nonrotating black holes, such as a Schwarzschild black hole. However, they fail to work in the Kerr spacetime because not all variables can be separable, or not all…
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 the results of a numerical investigation of charged-particle transport across a synthesized magnetic configuration composed of a constant homogeneous background field and a multiscale perturbation component simulating an effect…
We give a construction of completely integrable 4-dimensional Hamiltonian systems with cubic Hamilton functions. Applying to the corresponding pairs of commuting quadratic Hamiltonian vector fields the so called Kahan-Hirota-Kimura…
A novel symplectic integrator for Hamiltonian equations on $S_2^n \times T^{\ast} \RR^m$ is developed and studied. Partitioned Runge--Kutta methods for Hamiltonian systems on products of Hamiltionian manifolds are studied, specifically,…
In this paper an approach is outlined. With this approach some explicit algorithms can be applied to solve the initial value problem of $n-$dimensional damped oscillators. This approach is based upon following structure: for any…
The evolution of any factorized time-reversible symplectic integrators, when applied to the harmonic oscillator, can be exactly solved in a closed form. The resulting modified Hamiltonians demonstrate the convergence of the Lie series…
Modern synchrotron light sources are often characterized with high-brightness synchrotron radiation from insertion devices. Inevitably, insertion devices introduce nonlinear distortion to the beam motion. Symplectic tracking is crucial to…
We study how inexact nonlinear solvers lead to a loss of exact symplecticity in the Symplectic Euler (SE) and Stormer-Verlet (SV) schemes when applied to general nonseparable Hamiltonian systems. These schemes are implicit and require…
We solve elliptic systems of equations posed on highly heterogeneous materials. Examples of this class of problems are composite structures and geological processes. We focus on a model problem which is a second-order elliptic equation with…
Hamiltonian systems are one of the most important class of dynamical systems with a geometric structure called symplecticity and the numerical algorithms which can preserve such geometric structure are of interest. In this article we study…
Space-charge effects play an important role in high intensity particle accelerators and were studied using a variety of macroparticle tracking models. In this paper, we propose a symplectic particle-in-cell (PIC) model and compare this…
This paper presents a method for learning Hamiltonian dynamics from a limited set of data points. The Hamiltonian vector field is found by regularized optimization over a reproducing kernel Hilbert space of vector fields that are inherently…
This article explores some geometric and algebraic properties of the dynamical system which is represented by matrix differential equations arising from inertial navigation problems, such as the symplecticity and the orthogonality.…
Modern semiconductor detectors allow for charged particle tracking with ever increasing position resolution. Due to the reduction of the spatial hit uncertainties, multiple Coulomb scattering in the detector layers becomes the dominant…