We consider the existence and spectral stability of static multi-kink structures in discrete sine-Gordon equation, as a representative example family Klein-Gordon models. The multi-kinks are constructed using Lin's method from an alternating sequence well-separated kink antikink solutions. then locate point spectrum associated with these solutions by reducing problem to matrix equation. For $m$...

The aim of this study is to introduce a stress-based non-binary contact model missing in classical discrete element method (DEM). To tackle issue, force-displacement law generalized by utilizing the trace particle stress tensor make all contacts dependent on other and thus, account for multiple simultaneously acting single particle. Simulation results uniaxial confined (oedometric) compression ...

This thesis addresses the problem of estimating the state in multi-agent decision and control systems. In particular, a novel approach to state estimation is developed that uses partial order theory in order to overcome some of the severe computational complexity issues arising in multi-agent systems. Within this approach, state estimation algorithms are developed that enjoy provable convergenc...

This paper proposes a design method for discrete abstractions of nonlinear systems using multi-resolution quantizer, which is capable of handling state dependent approximation precision requirements. To this aim, we extend the notion of quantizer embedding, which has been proposed by the authors’ previous works as a transformation from continuous-state systems to discrete-state systems, to a mu...