On the dynamics of the Szekeres system

The gravitational Szekeres differential system is completely integrable with two rational first integrals and an additional analytical first integral. We describe the dynamics of the Szekeres system when one of these two rational first integrals is negative, showing that all the orbits come from the infinity of ${\mathbb{R}}^4$ and go to infinity.     

Hjelmslev quadrilateral central configurations

A Hjelmslev quadrilateral is a quadrilateral with two right angles at opposite vertices. Using mutual distances as coordinates, we show that any four-body central configuration forming a Hjelmslev quadrilateral must be a right kite configuration.     

Wave-based analysis of dual acoustic black holes for anechoic termination of shock testing devices

Shock testing is an important issue for the survivability of an equipment under shock environment in aerospace and military industries. One of the problems faced in conventional shock testing devices is the need for redesigning of the geometry whenever the responses to different shock environments are tested. To circumvent the redesigning processes, a structure with two ‘acoustic black holes (ABHs)’ on both ends, referred to as the beam with dual ABHs, is proposed as a shock testing device. The beam with dual ABHs is capable of simulating diverse shock environments by controlling the applied force because it can be regarded as an infinite beam at high frequency range with the aid of the anechoic terminations by the ABHs. To systematically investigate the beam with dual ABHs, we develop a wave-based method that uses the reflection matrix of an ABH to perform free and forced vibration analyses. From the analyses on frequency response function and shock response spectrum of the beam with dual ABH, it is suggested that the beam with dual ABHs is feasible as a semi-permanent shock testing device.     

Self‐Assembly of Uranyl–Peroxide Nanocapsules in Basic Peroxidic Environments

A wide range of uranyl–peroxide nanocapsules have been synthesized using very simple reactants in basic media; however, little is known about the process to form these species. We have performed a density functional theory study of the speciation of the uranyl ions under different experimental conditions and explored the formation of dimeric species via a ligand exchange mechanism. We shed some light onto the importance of the excess of peroxide and alkali counterions as a thermodynamic driving force towards the formation of larger uranyl–peroxide species.