Symplectic integrators are extensively used for single particle tracking in accelerators. A symplectic integrator scheme, which involves only positive steps, for perturbed Hamiltonians of the form H = A + B, where both A and B are integrable, was proposed [1], and all order of such integrators were derived [2]. A particular member of the family, namely the SABA2 integrator has already proved to...

We examine a new second-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, 1/2, is about 10 times smaller than that of the standard second-order leapfrog (2LF) integrator. As a result, the step size of the new integrator can be made about three times larger. Taking into account a facto...

The paper presents a summary of different double second-order generalized integrator (DSOGI)-based phase-locked loop (PLL) algorithms for synchronization with three-phase weak grids. methods are compared through simulation under variety grid conditions, such as unbalanced phase voltages, high low-order harmonics distortion, frequency steps, jumps, and voltage sags. Following the results, three ...

Abstract This article addresses the concern that decision-making in sexual orientation or gender identity (SOGI) asylum claims Europe is often unfair, and one way to remedy this by improving guidance provided decision-makers when interpreting Refugee Convention respect of these claims. We begin interrogating a number different guidelines models assess whether they contribute fairer system. show...

Abstract. We present a new class of high-order variational integrators on Lie groups. We show that these integrators are symplectic, momentum preserving, and can be constructed to be of arbitrarily high-order, or can be made to converge geometrically. Furthermore, these methods are stable and accurate for very large time steps. We demonstrate the construction of one such variational integrator ...

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 phase space of the elastic pendulum at higher order resonance, a numerical integrator which preserves qualitative features after long integration times is neede...