Abstract In this paper, we propose two projected dynamical systems for solving inverse quasi-variational inequality problems in finite-dimensional Hilbert spaces–one ensuring finite-time stability and the other guaranteeing fixed-time stability. We first establish the connection between these dynamical systems and the solutions of inverse quasi-variational problems. Then, under mild conditions on the operators and parameters, we analyze the finite-time and fixed-time stability of the proposed systems. Both approaches offer accelerated convergence; however, while the settling time of a finite-time stable dynamical system depends on initial conditions, the fixed-time stable system achieves convergence within a predefined time, independent of initial conditions. Furthermore,...

Abstract This study explores the crack opening dynamics in Mode-I fracture of pre-stretched viscoelastic elastomer sheets under varying strain energy release rate (Γ). The degree of viscoelasticity was widely tuned by altering the mixing ratio of telechelic precursor chains and a tri-functional cross-linker, producing elastomers with different amounts of relaxation components such as dangling chains and finite clusters not incorporated into infinite networks. When Γ exceeds a critical threshold Γ∗, the crack velocity exhibits a sharp, order-of-magnitude increase—independent of viscoelasticity—similar to that observed in conventional elastic elastomers. A key difference, however, emerges in the crack-tip opening displacement (CTOD): while elastic...

Abstract Pyrene belongs to the highly toxic class of polycyclic aromatic hydrocarbons and has carcinogenic properties; thus, the kinetics of its OH-initiated oxidation is theoretically investigated in a wide range of conditions (T = 200-2000 K and P = 7.6-76,000 Torr). The T & P-dependent kinetic behaviors were studied within the stochastic RRKM-based master equation framework with the potential energy profile constructed at the ROCBS-QB3//M06-2X/aug-cc-pVTZ level. The computed total rate constants ktotal are in good agreement with the laboratory values, thus helping resolve the discrepancy between the prior calculations and the measured values. The model reveals detailed mechanistic insights: (i) the OH-addition channels from the Cα and Cγ...