Resonances in bounded media: Nonlinear and boundary effects

We study the response of nonlinear wave systems in bounded domains at or near resonance. There are typically two qualitatively distinct types of response which may be observed relating to whether or not higher harmonics are themselves resonant. We introduce a variety of nonlinear model problems at or near resonance and study the subsequent response. We explain how the features of this problem such as the form of nonlinearity, boundary conditions, and the nature of spectrum play a fundamental role in the qualitative nature of the response. Numerical simulations are carried out to provide further explanation and comparison with analytic approximations. The results of this study provide a better understanding of the impact and interplay between nonlinear and boundary effects and thus in turn will contribute to providing new insights into various physically motivated problems in acoustics and other settings.     

Two questions on semi-clean group rings

It was proved in [4] that every group ring of a torsion abelian group over a commutative local ring is a semi-clean ring. It was asked in [4] whether every group ring of a torsion abelian group over a commutative clean ring is a semi-clean ring and whether every group ring of a torsion abelian group over a commutative semi-clean ring is a semi-clean ring. In this paper, we give a positive answer to question 1 and a negative answer to question 2.     

Infinite propagation speed of a weakly dissipative modified two-component Dullin–Gottwald–Holm system

We consider the infinite propagation speed of a weakly dissipative modified two-component Dullin–Gottwald–Holm (mDGH2) system. The infinite propagation speed is derived for the corresponding solution with compactly supported initial data that does not have compact support any longer in its lifespan.     

Reversible Solid–Solid Conversion of Sulfurized Polyacrylonitrile Cathodes in Lithium–Sulfur Batteries by Weakly Solvating Ether Electrolytes

Despite carbonate electrolytes exhibiting good stability to sulfurized polyacrylonitrile (SPAN), their chemical incompatibility with lithium (Li) metal anode leads to poor electrochemical performance of Li||SPAN full cells. While the SPAN employs conventional ether electrolytes that suffer from the shuttle effect, leading to rapid capacity fading. Here, we tailor a dilute electrolyte based on a low solvating power ether solvent that is both compatible with SPAN and Li metal. Unlike conventional ether electrolytes, the weakly solvating ether electrolyte enables SPAN to undergo reversibly “solid–solid” conversion. It features an anion–rich solvation structure that allows for the formation of a robust cathode electrolyte interphase on the SPAN, effectively blocking the dissolution of polysulfides into the bulk electrolyte and avoiding the shuttle effect. What's more, the unique electrolyte chemistry endowed Li ions with fast electroplating kinetics and induced high reversibility Li deposition/stripping process from 25 °C to −40 °C. Based on tailored electrolyte, Li||SPAN full cells matched with high loading SPAN cathodes (≈3.6 mAh cm⁻²) and 50 μm Li foil can operate stably over a wide range of temperatures. Additionally, Li||SPAN pouch cell under lean electrolyte and 5 % excess Li conditions can continuously operate stably for over a month.     

On the rate of convergence of solutions in free boundary problems via penalization

The rate of convergence of approximate solutions via penalization for free boundary problems are concerned. A key observation is to obtain global bounds of penalized terms which give necessary estimates on integrations by the nonlinear adjoint method by L.C. Evans.