We study the phase diagram of the isotropic J1–J ′ 1–J2 Heisenberg model for spin-1 particles on an anisotropic square lattice, using the coupled-cluster method. We find no evidence for an intermediate phase between the Néel and stripe states, as compared with all previous results for the corresponding spin-1/2 case. However, we find a quantum tricritical point at J ′ 1/J1 ≈ 0.66± 0.03, J2/J1 ≈...

The purpose of this rersearch is to analyze the effective application of particular earth orbits in dynamical modeling of relative motion problem between two spacecraft. One challenge in implementing these motions is maintaining the relations as it experiences orbital perturbations (zonal harmonics J2 and J3), most notably due to the Earth’s oblateness. Certain aspects of the orbital geometry c...

The free electron laser instability is investigated theoretically for a tenuous relativistic electron beam propagating parallel to a longitudinal wiggler field (Bo + 6Bainkoz)%. The stability analysis is based on the linearized Vlasov-Maxwell equations for perturbations about the beam equilibrium f4 = (nb/2w5)6(p_-mV)6(p,-mmV). For (W D/b)(eB/BO) of order unity or larger, it is found that the t...

This paper continues the authors’ previous study (SIAM J. Math. Anal., 2016) of the trend toward equilibrium of the Becker-Döring equations with subcritical mass, by characterizing certain fine properties of solutions to the linearized equation. In particular, we partially characterize the spectrum of the linearized operator, showing that it contains the entire imaginary axis in polynomially we...

We study the dynamics of perturbations in time-delay dynamical systems. Using a suitable space-time coordinate transformation, we find that the time evolution of the linearized perturbations (Lyapunov vector) can be described by the linear Zhang surface growth model [J. Phys. (France) 51, 2129 (1990)]], which is known to describe surface roughening driven by power-law distributed noise. As a co...

Orbit perturbations are fundamental when analyzing the long-term evolution and stability of natural or artificial satellites. We propose the computation of transfer maps for repetitive dynamical systems as a novel approach to study the long-term evolution of satellite and space debris motion. We provide two examples of this technique, the evolution of high area-to-mass ratio spacecraft under so...

An analysis of a synchronous generator in a bond graph approach is proposed. This bond graph allows to determine the simplified models of the system by using singular perturbations. Firstly, the nonlinear bond graph of the generator is linearized. Then, the slow and fast state equations by applying singular perturbations are obtained. Also, a bond graph to get the quasi-steady state of the slow...