Yang-Baxter operators and scattering amplitudes in N=4\mathcal{N} = 4 super-Yang-Mills theory

Yangian symmetry of amplitudes in $\mathcal{N}=4$ super Yang-Mills theory is formulated in terms of eigenvalue relations for monodromy matrix operators. The Quantum Inverse Scattering Method provides the appropriate tools to treat the extended symmetry and to recover as its consequences many known features like cyclic and inversion symmetry, BCFW recursion, Inverse Soft Limit construction, Grassmannian integral representation, $\mathrm{R}$-invariants and on-shell diagram approach.Comment: 32 pages, 10 figures, final version for publicatio

Preliminary Orbit Determination System (PODS) for Tracking and Data Relay Satellite System (TDRSS)-tracked target Spacecraft using the homotopy continuation method

The Preliminary Orbit Determination System (PODS) provides early orbit determination capability in the Trajectory Computation and Orbital Products System (TCOPS) for a Tracking and Data Relay Satellite System (TDRSS)-tracked spacecraft. PODS computes a set of orbit states from an a priori estimate and six tracking measurements, consisting of any combination of TDRSS range and Doppler tracking measurements. PODS uses the homotopy continuation method to solve a set of nonlinear equations, and it is particularly effective for the case when the a priori estimate is not well known. Since range and Doppler measurements produce multiple states in PODS, a screening technique selects the desired state. PODS is executed in the TCOPS environment and can directly access all operational data sets. At the completion of the preliminary orbit determination, the PODS-generated state, along with additional tracking measurements, can be directly input to the differential correction (DC) process to generate an improved state. To validate the computational and operational capabilities of PODS, tests were performed using simulated TDRSS tracking measurements for the Cosmic Background Explorer (COBE) satellite and using real TDRSS measurements for the Earth Radiation Budget Satellite (ERBS) and the Solar Mesosphere Explorer (SME) spacecraft. The effects of various measurement combinations, varying arc lengths, and levels of degradation of the a priori state vector on the PODS solutions were considered

Determination of the Earth's pole tide Love number k₂ from observations of polar motion using an adaptive Kalman filter approach

The geophysical interpretation of observed time series of Earth rotation parameters (ERP) is commonly based on numerical models that describe and balance variations of angular momentum in various subsystems of the Earth. Naturally, models are dependent on geometrical, rheological and physical parameters. Many of these are weakly determined from other models or observations. In our study we present an adaptive Kalman filter approach for the improvement of parameters of the dynamic Earth system model DyMEG which acts as a simulator of ERP. In particular we focus on the improvement of the pole tide Love number k(2). In the frame of a sensitivity analysis k(2) has been identified as one of the most crucial parameters of DyMEG since it directly influences the modeled Chandler oscillation. At the same time k(2) is one of the most uncertain parameters in the model. Our simulations with DyMEG cover a period of 60 years after which a steady state of k(2) is reached. The estimate for k(2), accounting for the anelastic response of the Earth's mantle and the ocean, is 0.3531 + 0.0030i. We demonstrate that the application of the improved parameter k(2) in DyMEG leads to significantly better results for polar motion than the original value taken from the Conventions of the International Earth Rotation and Reference Systems Service (IERS)