# Keynote Speakers

 Wang Chien Ming National University of Singapore Title: Analogies between central finite difference, Hencky bar chain and Eringen’s nonlocal beam models for buckling and vibration. Abstract: This keynote lecture points out the analogies between the central finite difference beam model, Hencky bar-chain model and Eringen’s nonlocal beam model. The finite difference beam model is obtained by discretizing the differential governing equation of the beam via finite difference equations for approximating the derivatives. The Hencky bar-chain model comprises finite rigid beam segments connected by frictionless hinges with elastic rotational springs. Eringen’s nonlocal theory allows for the effect of small length scale effect which becomes significant when dealing with nanobeams. Based on the mathematically similarity of the governing equations of these three beam models, analogies exist between them. The consequence is that one could readily obtain the buckling and vibration solutions of beams without solving the differential equation as well as it allows one to calibrate Eringen’s small length scale coefficient $e_0$. As an example, for an initially stressed vibrating beam with simply supported ends, it is found via this analogy that Eringen’s small length scale coefficient $\sqrt{\frac{1}{6}-\frac{1}{12}\frac{\sigma_0}{\bar{\sigma_m}}}$ where $\sigma_0$ is the initial stress and $\bar{\sigma_m}$  is the m-th mode buckling stress of the corresponding local Euler beam. It is shown that $e_0$ varies with respect to the initial axial stress, from $1/\sqrt{12}$ at the buckling compressive stress to $1/\sqrt{6}$  when the axial stress is zero and it monotonically increases with increasing initial tensile stress. The small length scale coefficient $e_0$ however, does not depend on the vibration/buckling mode considered. Keywords: buckling, finite difference beam model, Hencky bar chain model, nonlocal beam theory, repetitive cells, small length scale coefficient, vibration Juan I. Ramos University of Malaga Title: Local linearization methods in space and time for nonlinear wave propagation. Abstract: In this keynote lecture, linearization methods for nonlinear ordinary (odes) and partial differential equations (pdes) are presented. For initial-value problems of odes, these linearization methods provide locally exponential solutions, whereas, for boundary-value problems of odes, local spatial linearization subject to continuity of the dependent variables and their first derivative provides locally analytical solutions. For one-dimensional transport equations, upon first discretizing the time derivative and then linearizing the resulting equations with respect to the previous time level, two-point nonlinear boundary-value problems are obtained. These problems become locally linear and integrable upon local linearization in space. For multidimensional problems, time discretization followed by time linearization and approximate factorization of the resulting multidimensional nonlinear elliptic problem into a sequence of one-dimensional ones yields nonlinear two-point boundary-value problems which upon local spatial linearization result in linear ones that have local analytical solutions. The advantages and disadvantages of time linearization are discussed in detail, and the methods are applied to solve initial-value problems of nonlinear dynamical systems including nonlinearities that are not differentiable, differentialdifference equations, delay equations, jerk dynamics, nonlinear two-point boundary-value problems with regular singular points at a boundary, one- and two-dimensional advectionreaction diffusion problems arising in combustion theory, one-dimensional nonlinear acoustic phenomena, and the break-up and formation of solitary waves from both the equalwidth and the generalized regularized-long wave equations. Comparisons between the results obtained with these methods and standard second-order accurate finite-difference discretization and three-point, compact, fourth-order accurate discretization of the spatial derivatives are also presented. Keywords: time linearization, local spatial discretization, nonlinear evolution equations, nonlinear wave propagation, reaction-diffusion equations, nonlinear dynamics Mohamed Guma El-Tarhuni American University of Sharjah Title: The Road to 5G Wireless Communications Systems Abstract:There have been tremendous developments in mobile radio communications systems over the past few decades as a response to the wide acceptance of wireless communication services including basic voice applications, higher date rates applications. We have witnessed an accelerated trend on adopting new technologies to support the ever increasing number of users and From basic voice call services, support of data applications, seamless worldwide connectivity, and enhanced Quality of Services. In this talk, we will present an overview of the recent developments in mobile radio systems as we move towards the fifth generation (5G) by the year 2020. The main features expected from 5G and targeted applications are highlighted. Finally, the enabling technologies and challenges facing 5G systems are discussed.