Differential equations on unitarity cut surfaces

We reformulate differential equations (DEs) for Feynman integrals to avoid doubled propagators in intermediate steps. External momentum derivatives are dressed with loop momentum derivatives to form tangent vectors to unitarity cut surfaces, in a way inspired by unitarity-compatible IBP reduction. For the one-loop box, our method directly produces the final DEs without any integration-by-parts reduction. We further illustrate the method by deriving maximal-cut level differential equations for two-loop nonplanar five-point integrals, whose exact expressions are yet unknown. We speed up the computation using finite field techniques and rational function reconstruction.Comment: 17 pages, 3 figures; v2: added more results and references, final journal versio

Dynamics of the Boxy Elliptical Galaxy NGC 1600

We use three--integral models to infer the distribution function (DF) of the boxy E3-E4 galaxy NGC 1600 from surface brightness and line profile data on the minor and major axes. We assume axisymmetry and that the mass-to-light ratio is constant in the central ~1 R_e. Stars in the resulting gravitational potential move mainly on regular orbits. We use an approximate third integral K from perturbation theory, and write the DF as a sum of basis functions in the three integrals E, L_z and K. We then fit the projected moments of these basis functions to the kinematic observables and deprojected density, using a non-parametric algorithm. The deduced dynamical structure is radially anisotropic, with sigma_theta/sigma_r ~ sigma_phi/sigma_r ~ 0.7 on the major axis. Both on the minor axis and near the centre the velocity distribution is more isotropic; thus the model is flattened by equatorial radial orbits. The kinematic data is fit without need for a central black hole; the central mass determined previously from ground-based data therefore overestimates the actual black hole mass. The mass-to-light ratio of the stars is M/L_V = 6 h_50. The anisotropy structure of NGC 1600 with a radially anisotropic main body and more nearly isotropic centre is similar to that found recently in NGC 1399, NGC 2434, NGC 3379 and NGC 6703, suggesting that this pattern may be common amongst massive elliptical galaxies. We discuss a possible merger origin of NGC 1600 in the light of these results.Comment: 14 pages, 9 figures, re-submitted to Monthly Notice

Effects of Impedance Reduction of a Robot for Wrist Rehabilitation on Human Motor Strategies in Healthy Subjects during Pointing Tasks

Studies on human motor control demonstrated the existence of simplifying strategies (namely `Donders' law') adopted to deal with kinematically redundant motor tasks. In recent research we showed that Donders' law also holds for human wrist during pointing tasks, and that it is heavily perturbed when interacting with a highly back-drivable state-of-the-art rehabilitation robot. We hypothesized that this depends on the excessive mechanical impedance of the Pronation/Supination (PS) joint of the robot and in this work we analyzed the effects of its reduction. To this end we deployed a basic force control scheme, which minimizes human-robot interaction force. This resulted in a 70% reduction of the inertia in PS joint and in decrease of 81% and 78% of the interaction torques during 1-DOF and 3-DOFs tasks. To assess the effects on human motor strategies, pointing tasks were performed by three subjects with a lightweight handheld device, interacting with the robot using its standard PD control (setting impedance to zero) and with the force-controlled robot. We quantified Donders' law as 2-dimensional surfaces in the 3-dimensional configuration space of rotations. Results revealed that the subject-specific features of Donders' surfaces reappeared after the reduction of robot impedance obtained via the force control

Extended Object Tracking: Introduction, Overview and Applications

This article provides an elaborate overview of current research in extended object tracking. We provide a clear definition of the extended object tracking problem and discuss its delimitation to other types of object tracking. Next, different aspects of extended object modelling are extensively discussed. Subsequently, we give a tutorial introduction to two basic and well used extended object tracking approaches - the random matrix approach and the Kalman filter-based approach for star-convex shapes. The next part treats the tracking of multiple extended objects and elaborates how the large number of feasible association hypotheses can be tackled using both Random Finite Set (RFS) and Non-RFS multi-object trackers. The article concludes with a summary of current applications, where four example applications involving camera, X-band radar, light detection and ranging (lidar), red-green-blue-depth (RGB-D) sensors are highlighted.Comment: 30 pages, 19 figure

Wrinkling in engineering fabrics: a comparison between two different comprehensive modelling approaches

We consider two ‘comprehensive’ modelling approaches for engineering fabrics. We distinguish the two approaches using the terms ‘semi-discrete’ and ‘continuum’, reflecting their natures. We demonstrate a fitting procedure, used to identify the constitutive parameters of the continuum model from predictions of the semi-discrete model, the parameters of which are in turn fitted to experimental data. We, then, check the effectiveness of the continuum model by verifying the correspondence between semi-discrete and continuum model predictions using test cases not previously used in the identification process. Predictions of both modelling approaches are compared against full-field experimental kinematic data, obtained using stereoscopic digital image correlation techniques, and also with measured force data. Being a reduced order model and being implemented in an implicit rather than an explicit finite-element code, the continuum model requires significantly less computational power than the semi-discrete model and could therefore be used to more efficiently explore the mechanical response of engineering fabrics

Generation and Calibration of Linear Models of Aircraft with Highly Coupled Aeroelastic and Flight Dynamics

The lightweight structures and unconventional configurations being considered for the next generation of aircraft mean that any effort to predict or control the flight dynamics is impacted by the structural dynamics. One of the most severe forms of coupling between aeroelasticity and flight dynamics is an instability called body freedom flutter. The existing tools often assume a relatively weak effect of structural dynamics on the flight dynamics, and are therefore incapable of modeling strong interactions like body freedom flutter. A method of combining different sources of data traditionally used for aeroelasticity and flight dynamics is described by reconciling many of the differences between these models. By building upon past modeling efforts, a level of familiarity in the approach is achieved. Generally the differences from the traditional approaches are subtle but significant. The traditional frequency domain flutter model in a modal coordinate system is converted to a form consistent with a time domain flight dynamics model. The time domain rational function approximation about a non-inertial coordinate system and the unique constraints for the conversion between the inertial and non-inertial coordinate systems are discussed. A consistent transformation of the states of aeroelastic models to flight dynamics models is derived, which enables the integration of data from higher fidelity computational fluid dynamics models or wind-tunnel testing. The present method of integrating multidisciplinary data was used to create models that compare well with X-56A flight-test data, including conditions past the flutter speed