In the present study an alternative model allows the extension of the Debye-Hückel Theory (DHT) considering time dependence explicitly. From the Electro-Quasistatic approach (EQS) done in earlier studies time dependent potentials are suitable to describe several phenomena especially conducting media as well as the behaviour of charged particles in arbitrary solutions acting as electrolytes. Thi...

Nonlinear contraction theory allows surprisingly simple analysis of synchronisation phenomena in distributed networks of coupled nonlinear elements. The key idea is the construction of a virtual contracting system whose particular solutions include the individual subsystems’ states. We also study the role, in both nature and system design, of co-existing “power” leaders, to which the networks s...

Nonlinear phenomena play a crucial role in applied mathematics and physics. Analytic solutions of nonlinear equations are of fundamental importance and various methods for obtaining analytic solutions have been proposed. In this paper an application of the Adomian decomposition method is introduced for solving nonlinear fractional equations. The results reveal that the proposed method is very e...

In recent years, underactuated nonlinear dynamic systems trajectory tracking, such as space robots and manipulators with structural flexibility, has become a major field of interest due to the complexity and high computational load of these systems. Hierarchical sliding mode control has been investigated recently for these systems; however, the instability phenomena will possibly occur, especia...

Many of the physical phenomena, like friction, backlash, drag, and etc., which appear in mechanical systems are inherently nonlinear and have destructive effects on the control systems behavior. Generally, they are modeled by hard nonlinearities. In this paper, two different methods are proposed to cope with the effects of hard nonlinearities which exist in friction various models. Simple inver...

We observe experimentally a novel type of nonlinear diffraction in the process of two-wave mixing on a nonlinear quadratic grating. We demonstrate that when the nonlinear grating is illuminated simultaneously by two noncollinear beams, a second-harmonic diffraction pattern is generated by a virtual beam propagating along the bisector of the two pump beams. The observed diffraction phenomena is ...

Title of dissertation: ADVANTAGEOUS UTILIZATION OF NONLINEAR PHENOMENA IN MICRO-STRUCTURES AND MACRO-STRUCTURES Andrew James Dick, Doctor of Philosophy, 2007 Dissertation directed by: Professor Balakumar Balachandran and Professor C. Daniel Mote, Jr. Department of Mechanical Engineering Within this work, the nonlinear oscillations of various beam-like structures are studied. Methods are develop...