Dr Gihane Nasr and Dr Hassan Saoud, associate professors at the Lebanese University – Faculty of Science has been selected by the J. William Fulbright Foreign Scholarship Board for two Fulbright Grant (two from three grants for Lebanon) under the provision of the Fulbright Program. Those grants are administered by the Bureau of Educational and Cultural Affairs, United Stated Department of State with the cooperation of the Council for International Exchange of Scholars.
Dr Nasr will be hosted at the University of Michigan – Ann Arbor for 7 months. Her project deals with the “Encapsulation of Frangrances in PAMAM Dendrimers to Preserve Essential Oils Properties: Application to Linalool”. In order to improve human quality life, essential oils (EOs) is used as alternatives for synthetic harmful molecules. Dr Nasr proposes to encapsulate linalool in the interior voids of poly(amidoamine) PAMAM dendrimers. This nanotechnological approach may resolve the problem of instability, volatility and poor aqueous solubility of the components in EOs. Various parameters will be tested to define the optimal conditions of the preparation of this nanostructures. Encapsulation through dendrimers is a promising strategy to increase the shelf-life of bioactive molecules which may find applications in cosmetics, food and drug industries.
Dr Saoud will be hosted at Michigan State University for 6 months. His project tackles the “Study of Nonsmooth Dynamical Systems”. In fact, differential equations with non-smooth components occur in various situations. For example, they arise in mechanical systems if the effects of dry friction are included into the model, or they occur in the case of impacts. They are present in electrical circuits or in biological systems, if the non-smooth characteristics are used to represent switches. Discontinuous dynamical systems arise in a large number of applications. In optimal control problems, open-loop bang-bang controllers switch discontinuously between extreme values of the inputs to generate minimum-time trajectories from the initial to the final states. In his project, Dr Saoud will be interested to study the stability of an important class on non-smooth dynamical systems, called Evolution Variational Inequalities and Evolution Hemivariational Inequalities. The most important stability concept is stability in the sense of Lyapunov. Lyapunov's method is based on the study of the behavior of special functions called Lyapunov's function. This method avoids the calculation of an explicit solution of the problem. But, it requires to find a good Lyapunov candidates functions compatible with the problem, and the disadvantage is that there is no straightforward construction of Lyapunov functions.