Spiraling solutions of nonlinear Schrödinger equations

We study a new family of sign-changing solutions to the stationary nonlinear Schrödinger equation \[ -\Delta v +q v =|v|^{p-2} v, \qquad \text{in}\,{ {\mathbb{R}^{3}},} \] with $2 < p < \infty$ and $q \ge 0$ . These solutions are spiraling in the sense that they are not axially symmetric but invariant under screw motion, i.e., they share the symmetry properties of a helicoid. In addition to existence results, we provide information on the shape of spiraling solutions, which depends on the parameter value representing the rotational slope of the underlying screw motion. Our results complement a related analysis of Del Pino, Musso and Pacard in their study (2012, Manuscripta Math., 138, 273–286) for the Allen–Cahn equation, whereas the nature of results and the underlying variational structure are completely different.

Study of centrifugal rotary processing of parts in granular media

The results of centrifugal-rotary processing simulation of parts in granular media are presented. Model of the process at the microlevel — the movement of single particle of the medium and at the macrolevel — at the level of complex toroidal-screw motion of the medium in the working chamber is considered. Dependences used for simulation and determination of quantitative regularities are given.

Control Strategy of Screw Motion During Plasticizing Phase for All-Electric Injection Molding Machine

This work studies a control strategy of screw motion to improve the plasticizing precision for an all-electric injection molding machine (AIMM) based on a biaxial simultaneous motion system. In the standard plasticizing process, a screw retraction before or after the metering phase is proposed to link up with the traditional metering process for reducing the residual pressure at the end of holding and metering, respectively. The modified incomplete plasticizing process is then applied to prevent the potential over-travel of the screw. The incomplete plasticizing process uses a control strategy to obtain a fixed start point for the screw at injection in each cycle. Experimental results showed that both the standard and incomplete plasticizing process improve the visual quality and molded precision of parts.

Large deployable network constructed by Altmann linkages

This study proposes a large-scale modular deployable mechanical network constructed by networking Altmann linkages, which are spatial single-loop mechanisms with six revolute joints and four bars, and develops a theoretical approach to verify the feasibility of the networking method. First, the screw motion equation of the linkage is derived, and the deployability of the linkage is demonstrated through a motion simulation. Second, using the overlapping-unit method, a deployable mechanical network is constructed. The constraint graph of the mechanical network is deduced subsequently. The mobility of the mechanical network is proved by screw theory, which demonstrates the feasibility of the networking method. Then, the motion of the mechanical network is simulated and it is found to have excellent deployability. Finally, a prototype of the mechanical network is fabricated. Results show that spatial single-loop linkages can construct modular deployable mechanical networks with the overlapping-unit method under appropriate connections. This networking method can be verified with the theoretical approach proposed in this work.

Product Submanifold Based Analysis of Kinematic Chains and a 3-PUP Parallel Mechanism

The five types of kinematic chains that generate the planar motion group SE(2) of dimension three, with the prismatic-joint direction always perpendicular with the revolute-joint axis in each chain, have shown their effectiveness and manifested the charm in type synthesis and mechanism analysis in parallel mechanisms. This paper extends the traditional PRP kinematic chain generating the planar motion group SE(2) to a relatively general case, in which one of the prismatic joint-direction is not necessarily perpendicular with the revolute-joint axis, leading to the discovery of a screw motion with a variable pitch in this kinematic chain. Following the extraction of a screw motion from this particular PRP kinematic chain, this paper presents the bifurcated motion in a 3-PUP parallel mechanism by changing the active geometrical constraint in its configuration space, with a Lie group approach and interpretation. The constraint-singularity configuration sets for bifurcation of the 3-PUP parallel mechanism. The paper hence provides a Lie group representation and geometry interpretation for the kinematic equivalence of serial chains and the bifurcated motion of a parallel mechanism.

Magnetic curves in a Euclidean space: One example, several approaches

This is a short review of different approaches in the study of magnetic curves for a certain magnetic field and on the fixed energy level. We emphasize them in the case when the magnetic trajectory corresponds to a Killing vector field associated to a screw motion in the Euclidean 3-space.