A closed subgroup $H$ of a locally compact group $G$ is confined if the closure conjugacy class in Chabauty space does not contain trivial subgroup. We establish dynamical criterion on action totally disconnected $X$ ensuring that no relatively amenable can be confined. This property equivalent to fact its Furstenberg boundary free. Our applies Neretin groups. deduce each has two inequivalent i...

We present a guide to compute the phase-boundaries of classical systems using dynamic Clausius–Clapeyron integration (dCCI) method within LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) code. The advantage dCCI is because it provides coexistence curves spanning wide range thermodynamic states relatively short single non-equilibrium simulations. describe state-of-the-art free-...

This paper concerns the monostable cooperative system with nonlocal diffusion and free boundaries, which has recently been discussed by Du Ni [J. Differential equations 308(2021) 369-420 arXiv:2010.01244]. We here aim at four aspects: first is to give more accurate estimates for longtime behaviours of solution; second discuss limits solution pair a semi-wave problem; third investigate asymptoti...

In this short paper, based on the long range dispersal and environmental carrying capacity, we propose a new SIR epidemic model discuss its dynamic properties. The results show that disease will always spread if basic reproduction number $ \mathcal{R}_0(\theta/b,\,(-h_0,h_0))\ge 1 $; however, when \mathcal{R}_0(\theta/b,\,(-h_0,h_0))<1 $, whether spreading or vanishing depends expansion abil...