On the Existence of Linearly Oscillating Galaxies

We consider two classes of steady states of the three-dimensional, gravitational Vlasov-Poisson system: the spherically symmetric Antonov-stable steady states (including the polytropes and the King model) and their plane symmetric analogues. We completely describe the essential spectrum of the self-adjoint operator governing the linearized dynamics in the neighborhood of these steady states. We also show that for the steady states under consideration, there exists a gap in the spectrum. We then use a version of the Birman-Schwinger principle first used by Mathur to derive a general criterion for the existence of an eigenvalue inside the first gap of the essential spectrum, which corresponds to linear oscillations about the steady state. It follows in particular that no linear Landau damping can occur in the neighborhood of steady states satisfying our criterion. Verification of this criterion requires a good understanding of the so-called period function associated with each steady state. In the plane symmetric case we verify the criterion rigorously, while in the spherically symmetric case we do so under a natural monotonicity assumption for the associated period function. Our results explain the pulsating behavior triggered by perturbing such steady states, which has been observed numerically.

A 3D-Printable Robotic Gripper Based on Thick Panel Origami

Origami has been a source of inspiration for the design of robots because it can be easily produced using 2D materials and its motions can be well quantified. However, most applications to date have utilised origami patterns for thin sheet materials with a negligible thickness. If the thickness of the material cannot be neglected, commonly known as the thick panel origami, the creases need to be redesigned. One approach is to place creases either on top or bottom surfaces of a sheet of finite thickness. As a result, spherical linkages in the zero-thickness origami are replaced by spatial linkages in the thick panel one, leading to a reduction in the overall degrees of freedom (DOFs). For instance, a waterbomb pattern for a zero-thickness sheet shows multiple DOFs while its thick panel counterpart has only one DOF, which significantly reduces the complexity of motion control. In this article, we present a robotic gripper derived from a unit that is based on the thick panel six-crease waterbomb origami. Four such units complete the gripper. Kinematically, each unit is a plane-symmetric Bricard linkage, and the gripper can be modelled as an assembly of Bricard linkages, giving it single mobility. A gripper prototype was made using 3D printing technology, and its motion was controlled by a set of tendons tied to a single motor. Detailed kinematic modelling was done, and experiments were carried out to characterise the gripper’s behaviours. The positions of the tips on the gripper, the actuation force on tendons, and the grasping force generated on objects were analysed and measured. The experimental results matched well with the analytical ones, and the repeated tests demonstrate that the concept is viable. Furthermore, we observed that the gripper was also capable of grasping non-symmetrical objects, and such performance is discussed in detail in the paper.

A New Approach to Preform Design in Metal Forging Processes Based on the Convolution Neural Network

This study presents an innovative methodology for preform design in metal forging processes based on the convolution neural network (CNN) algorithm. The proposed approach extracts the features of inputted forging product geometries and utilizes them to derive the corresponding preform shapes by employing weight arrays (filters) determined during the convolutional operations. The filters are progressively updated during the training process, emulating the learning steps of a process engineer responsible for the design of preform shapes for the forging processes. The design system is composed of multiple three-dimensional (3D) CNN sub-models, which can automatically derive individual 3D preform design candidates. It also implies that the 3D surfaces of preforms are easily acquired, which is important for the forging industry. The proposed preform design methodology was validated by applying it to two-dimensional (2D) axisymmetric shapes, one-quarter plane-symmetric 3D shapes, and two other industrial cases. In all the considered cases, the design methodology achieved substantial reductions in the forging load without forging defects, proving its reliability and effectiveness for application in metal forging processes.

Emerging symmetric strain response and weakening nematic fluctuations in strongly hole-doped iron-based superconductors

Electronic nematicity is often found in unconventional superconductors, suggesting its relevance for electronic pairing. In the strongly hole-doped iron-based superconductors, the symmetry channel and strength of the nematic fluctuations, as well as the possible presence of long-range nematic order, remain controversial. Here, we address these questions using transport measurements under elastic strain. By decomposing the strain response into the appropriate symmetry channels, we demonstrate the emergence of a giant in-plane symmetric contribution, associated with the growth of both strong electronic correlations and the sensitivity of these correlations to strain. We find weakened remnants of the nematic fluctuations that are present at optimal doping, but no change in the symmetry channel of nematic fluctuations with hole doping. Furthermore, we find no indication of a nematic-ordered state in the AFe2As2 (A = K, Rb, Cs) superconductors. These results revise the current understanding of nematicity in hole-doped iron-based superconductors.