Classical observables from coherent-spin amplitudes

The quantum field-theoretic approach to classical observables due to Kosower, Maybee and O’Connell provides a rigorous pathway from on-shell scattering amplitudes to classical perturbation theory. In this paper, we promote this formalism to describe general classical spinning objects by using coherent spin states. Our approach is fully covariant with respect to the massive little group SU(2) and is therefore completely synergistic with the massive spinor-helicity formalism. We apply this approach to classical two-body scattering due gravitational interaction. Starting from the coherent-spin elastic-scattering amplitude, we derive the classical impulse and spin kick observables to first post-Minkowskian order but to all orders in the angular momenta of the massive spinning objects. From the same amplitude, we also extract an effective two-body Hamiltonian, which can be used beyond the scattering setting. As a cross-check, we rederive the classical observables in the center-of-mass frame by integrating the Hamiltonian equations of motion to the leading order in Newton’s constant.

UNCERTAINTY ANALYSIS OF SUB-EXERCISES IN UAM-SFR BENCHMARK WITH THE MCS CODE

Uncertainty analysis in Modelling (UAM) for Design, Operation and Safety Analysis of Sodium-cooled Fast Reactors (SFRs) has been formed by OECD/NEA to assess the effect of nuclear data uncertainties on parameters of interest in SFR analysis. In this paper, sub-exercises of a medium 1000 MWth metallic core (MET-1000) and a large 3600 MWth oxide core (MOX-3600) are tested by a Monte Carlo code MCS to perform uncertainty analysis. Classical perturbation theory and generalized perturbation theory are used to calculate sensitivity coefficients. Uncertainty is calculated by multiplying the sensitivity coefficients and relative covariance matrix from ENDF/B-VII.1 library.

Kramers' theory for diffusion on a periodic potential

Kramers' turnover theory, based on the dynamics of the collective unstable normal mode (also known as PGH theory), is extended to the motion of a particle on a periodic potential interacting bilinearly with a dissipative harmonic bath. This is achieved by considering the small parameter of the problem to be the deviation of the collective bath mode from its value along the reaction coordinate, defined by the unstable normal mode. With this change, the effective potential along the unstable normal mode remains periodic, albeit with a renormalized mass, or equivalently a renormalized lattice length. Using second order classical perturbation theory, this not only enables the derivation of the hopping rates and the diffusion coefficient, but also the derivation of finite barrier corrections to the theory. The analytical results are tested against numerical simulation data for a simple cosine potential, ohmic friction, and different reduced barrier heights.

Topological effect of surface plasmon excitation in gapped isotropic topological insulator nanowires

We present a theoretical investigation of the surface plasmon (SP) at the interface between a topologically nontrivial cylindrical core and a topologically trivial surrounding material, from the axion electrodynamics and modified constitutive relations. We find that the topological effect always leads to a red-shift of SP energy, while the energy red-shift decreases monotonically as core diameter decreases. A qualitative picture based on classical perturbation theory is given to explain these phenomena, from which we also infer that to enhance the shift, the difference between the inverse of dielectric constants of two materials must be increased. We also find that the surrounding magnetic environment suppresses the topological effect. All these features can be well described by a simple ansatz surface wave, which is in good agreement with full electromagnetic eigenmodes. In addition, bulk plasmon energy at ωp = 17.5 ± 0.2 eV for a semiconducting Bi2Se3 nanoparticle is observed from high-resolution electron energy loss spectrum measurements.

SDRE Control Applied to an Electromechanical Pendulum Excited by a Non-Ideal Motor

The dynamical behavior of an electromechanical pendulum system is analyzed by means of the classical perturbation theory. A frequency response model of the system is obtained, and the number of unstable poles are determined with the Routh-Hurwitz criterion. Numerical simulations show that the system presents nonlinear behavior such as hysteresis, with hard and soft characteristics, and the Sommerfeld effect in the resonance region. In order to keep the oscillations of the electromechanical system in a pre-defined amplitude range a control strategy is designed. The SDRE control strategy is used considering two control signals, a feedback control that tracks the system to a desired periodic orbit, and a nonlinear feedforward control that holds the system to that desired periodic orbit. Additionally, the robustness of the control technique is tested for parametric uncertainties. Numerical simulations show the efficiency of the control strategy.