Global solution to a three-dimensional spherical piston problem for the relativistic Euler equations

The study of spherically symmetric motion is important for the theory of explosion waves. In this paper, we consider a ‘spherical piston’ problem for the relativistic Euler equations, which describes the wave motion produced by a sphere expanding into an infinite surrounding medium. We use the reflected characteristics method to construct a global piecewise smooth solution with a single shock of this spherical piston problem, provided that the speed of the sphere is a small perturbation of a constant speed.

Period-3 Motions in a Parametrically Exited Inverted Pendulum

In this paper, period-3 motions in a parametrically exited inverted pendulum are analytically investigated through a discrete implicit mapping method. The corresponding stability and bifurcation conditions of the period-3 motions are predicted through eigenvalue analysis. The symmetric and asymmetric period-3 motions are obtained on the bifurcation tree, and the period-doubling bifurcations of the asymmetric period-3 motions are observed. The saddle-node and Neimark bifurcations for symmetric period-3 motions are obtained. The saddle-bifurcations of the symmetric period-3 motions are for symmetric motion appearance (or vanishing) and onsets of asymmetric period-3 motion. Numerical simulations of the period-3 motions in the inverted pendulum are completed from analytical predictions for illustration of motion complexity and characteristics.

Zero-point energy and photon spin-induced diffraction phenomena

A brief review of our previously introduced forward and backward in time formalism for non-relativistic electron diffraction and its relativistic extension to study photons in time and space is presented. The zero-point energy in the Planck black body spectrum emerges naturally once time-symmetric motion — inherent in Maxwell equations — is invoked for photons. A study of two-slit experiments for slits smaller than the wavelength of the photon unravels novel phenomena due to the spin of the photon. Our proposed experiments are within reach of present technology and could be of interest for modern imaging and quantum optics.

Kinetic Analysis of Water Fitness Exercises: Contributions for Strength Development

The evaluation of propulsive forces in water allows the selection of the most appropriate strategies to develop strength during water fitness sessions. The aim of this study was threefold: (i) to analyze the rate of force production; (ii) to analyze the rate of force variation; and (iii) to compare limbs’ symmetry in two water fitness exercises. Twenty-two young health subjects (age: 21.23 ± 1.51 years old, body mass: 67.04 ± 9.31 kg, and height: 166.36 ± 8.01 cm) performed incremental protocols of horizontal adduction (HA) and rocking horse (RHadd), from 105 until 150 b·min–1. Data acquisition required an isokinetic dynamometer and a differential pressure system that allowed the assessment of (a) isometric peak force of dominant upper limb (IsometricFD); (b) propulsive peak force of dominant upper limb (PropulsiveFD); and (c) propulsive peak force of nondominant upper limb (PropulsiveFND). Significant differences were found in the rate of force production (RateFD) between the majority cadences in both exercises. The RateFD reached ~68% of the force in dry-land conditions, and lower cadences promoted a higher rate of force variation (ΔForce). Most actions were asymmetric, except for the HA at 135 b·min–1. In conclusion, the musical cadence of 135 b·min–1 seems to elicit a desired rate of force production with a symmetric motion in both exercises.

Three Novel Symmetric Waldron–Bricard Metamorphic and Reconfigurable Mechanisms and Their Isomerization

This paper explores a class of metamorphic and reconfigurable linkages belonging to both Waldron's double-Bennett hybrid linkage and Bricard linkages, which include three novel symmetric Waldron–Bricard metamorphic and reconfigurable mechanisms, and further presents their three extended isomeric metamorphic linkages. The three novel Waldron–Bricard metamorphic and reconfigurable linkages are distinguished by line-symmetric, plane-symmetric, and line-plane-symmetric characteristics. The novel line-symmetric Waldron–Bricard metamorphic linkage with one Waldron motion branch and two general and three special line-symmetric Bricard motion branches is obtained by integrating two identical general Bennett loops. The novel plane-symmetric Waldron–Bricard reconfigurable linkage with two plane-symmetric motion branches is obtained by coalescing two equilateral Bennett loops. The novel line-plane-symmetric Waldron–Bricard metamorphic linkage with six motion branches is obtained by blending two identical equilateral Bennett loops, including the plane-symmetric Waldron motion branch, the line-plane-symmetric Bricard motion branch, the spherical 4R motion branch, and three special line-symmetric Bricard motion branches. With the isomerization that changes a mechanism structure but keeps all links and joints, each of the three novel Waldron–Bricard linkages results in an extended isomeric metamorphic linkage. This further evolves into the study of the three isomeric mechanisms. The study of these three novel metamorphic and reconfigurable mechanisms and their isomerization are carried out to demonstrate the characteristics of bifurcation and to reveal motion-branch transformation. Furthermore, by exploring the intersection of given motion branches and using the method of isomerization, more metamorphic and reconfigurable linkages can be discovered to usefully deal with transitions among possible submotions.

Numerical Study of Batoid with Asymmetrically Undulating Pectoral Fins

This paper presents a numerical study of three dimensional flows around a self-propelled batoid with asymmetrically undulating pectoral fins. During the dynamic simulation, the difference of phase angle of the asymmetric motion is set to 180° between left pectoral fin and right pectoral fin. To evaluate the swimming performance of batoid with asymmetric undulating fins, kinematic and dynamic parameters have been used comparing with that of batoid with symmetric undulating fins. The simulation results show that asymmetric motion can achieve better starting and accelerating performance than symmetric motion.