We define an imperative programming language, which extends while programs with a type for storing atoms or hereditarily orbit-finite sets. To deal with an orbit-finite set, the language has a loop construction, which is executed in parallel for all elements of an orbit-finite set. We show examples of programs in this language, e.g. a program for minimising deterministic orbit-finite automata. ...

Canonical perturbation theory shows that orbit-averaged theory only requires the time-scale separation between equilibrium and perturbed motions and verifies the conventional concept that orbit averaging effects greatly reduce the transport of energetic particles by microturbulence in tokamak. Thereafter, a recent claim [Phys. Rev. Lett. 102, 075004 (2009); 107, 239502 (2011)] of the orbit-aver...

Taking into account spin-spin (SS), spin-other-orbit (SOO), and orbit-orbit (OO) interactions in addition to general spin-orbit (SO) interactions, the local structures of Ni2+ in CsMgX3 (X = Cl, Br, I) are theoretically investigated by using the complete diagonalization method (CDM). On this basis, it is found that the local angles, at the Ni2+ centres are larger than those, at the hosts. The c...

We propose a method to improve spin-orbit potentials of the Skyrme interaction in N > Z nuclei. New spin-orbit parameters for Skyrme interactions SIII, SkM∗ and SGII are shown to yield better agreement with empirical spin-orbit splittings than the original ones, not only in 16O but also in 208Pb. The isotope shifts in Pb nuclei and excitation energies of collective Gamow-Teller states in 48Sc, ...

The general tensorial form of the orbit–orbit interaction operator in the formalism of second quantization is presented. Such an expression is needed to calculate both diagonal and off–diagonal matrix elements with respect to configurations, in a uniform way. Some special cases are shown for which the orbit–orbit interaction operator reduces to simple form. The importance of different contribut...

The APS Real-Time Orbit Feedback System is designed to stabilize the orbit of the stored positron beam against low-frequency sources such as mechanical vibration and power supply ripple. A distributed array of digital signal processors is used to measure the orbit and compute corrections at a 1kHz rate. The system also provides extensive beam diagnostic tools. This paper describes the architect...

The molecule-like structure of C isotopes (A = 12, 14, 16) is investigated using a microscopic α+α+α+n+n+·· model. The valence neutrons are classified based on the molecular-orbit (MO) model, and both π-orbit and σ-orbit are introduced around three α-clusters. The combination of the valence neutrons in the πand the σ-orbit is promising to stabilize the linear-chain state against the breathing a...

A new guidance scheme for the problem of Low-thrust transfer between inclined orbits is developed within the framework of optimal control theory. The objective of the guidance scheme is to provide the appropriate thrust steering program that will transfer the vehicle from an inclined low earth orbits to the high earth orbits. The presented guidance scheme is determined using Pontryagin’s princi...

The applicability of advanced numerical methods for the solution of the orbit determination problem is studied. The dynamics of the observed object is written as a system of integral equations. This system is solved numerically by representing the components of the force function as linear combinations of B-splines and by applying the multigrid technique. In an outer loop the orbit determinatio...