Negash G. Medhin

Multiscale Considerations in Modeling of Nonlinear Elastomers

We present a survey of results from an extended project focused on the understanding of the dynamic behavior of elastomers or filled rubbers. This entailed experimental, modeling, computational and theoretical efforts. Of particular emphasis are the nonlinear and hysteretic aspects of dynamic deformations.

Leader-follower games in marketing: a differential game approach

In normal differential game models, players are assumed to make decisions simultaneously. Thus, a competitor does not know the decision policies of others as he decides on his own strategy or control. However, in reality, it is not unusual for competitors to make decisions at different times. Thus, the roles of competitors are not always the same. Some competitors have priority in making decisions of policy over others. Those who make decisions first are called leaders, the others are called followers. This type of game is called Leader-Follower (L-F) or Stackelberg game. The solution of such a game is no longer in terms of Nash equilibrium. In this paper, we consider an L-F differential game to model competition in the final stage of a product life cycle in a non-symmetric market environment, derive and solve the optimality conditions in terms of a new definition of solution.

Mathematical model for a laminated curved beam

We present a mathematical framework to provide general well-posedness and approximation results for a laminated curved beam. The model includes unbounded inputs from the piezoceramic patches, hysteresis and shear in the viscoelastic layers. The viscoelastic layers are held in place by sandwiching them between the elastic core and elastic constraining layers. Families of linear and cubic splines are used to illustrate the approximation ideas.