scholarly journals High-order nonlinearity of silica-gold nanoshells in chloroform at 1560 nm

2010 ◽  
Vol 18 (21) ◽  
pp. 21636 ◽  
Author(s):  
E. L. Falcão-Filho ◽  
R. Barbosa-Silva ◽  
R. G. Sobral-Filho ◽  
A. M. Brito-Silva ◽  
A. Galembeck ◽  
...  
Keyword(s):  
High Order ◽  
Gold Nanoshells ◽  
High Order Nonlinearity

Analysis of Z-scan of thick media with high-order nonlinearity by variational approach

2003 ◽  
Vol 219 (1-6) ◽  
pp. 411-419 ◽  
Author(s):  
Zhibo Liu ◽  
Weiping Zang ◽  
Jianguo Tian ◽  
Wenyuan Zhou ◽  
Chunping Zhang ◽  
...  
Keyword(s):  
Variational Approach ◽  
High Order ◽  
High Order Nonlinearity

scholarly journals Controlling the dynamics of Burgers equation with a high-order nonlinearity

2004 ◽  
Vol 2004 (62) ◽  
pp. 3321-3332 ◽  
Author(s):  
Nejib Smaoui
Keyword(s):  
Steady State ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Nonlinear Boundary ◽  
Burgers Equation ◽  
High Order ◽  
Time Stepping ◽  
Backward Euler ◽  
High Order Nonlinearity ◽  
Steady State Solutions

We investigate analytically as well as numerically Burgers equation with a high-order nonlinearity (i.e.,ut=νuxx−unux+mu+h(x)). We show existence of an absorbing ball inL2[0,1]and uniqueness of steady state solutions for all integern≥1. Then, we use an adaptive nonlinear boundary controller to show that it guarantees global asymptotic stability in time and convergence of the solution to the trivial solution. Numerical results using Chebychev collocation method with backward Euler time stepping scheme are presented for both the controlled and the uncontrolled equations illustrating the performance of the controller and supporting the analytical results.

Steady-State Dynamics of Smooth and Non-Smooth Systems With Strong Nonlinearities

2003 ◽  
Author(s):  
Xiaoai Jiang ◽  
Alexander F. Vakakis
Keyword(s):  
Steady State ◽  
Vibration Isolation ◽  
High Order ◽  
State Behavior ◽  
Energy Pumping ◽  
Nonlinear Energy Pumping ◽  
Clearance Nonlinearity ◽  
High Order Nonlinearity ◽  
Odd Nonlinearity ◽  
Nonlinear Energy

The nonlinear energy sinks (NESs) with strong essential stiffness nonlinearities have been shown to result in vibration isolation in the studied system. In comparison, we also studied the steady-state dynamic response of a system with its smooth high-order odd nonlinearity replaced with the best fitted nonsmooth “clearance nonlinearity”. The analysis was based on the complexification technique and the separation of the dynamic terms into the “slow-varying” and the “fast-varying” components. We found that the steady-state behavior of a system with the non-smooth NES resembles that of the system with the smooth high-order nonlinearity, preserving the nonlinear energy-pumping feature. This finding paves the way for constructing practical NESs and applying them to practical vibration-isolation problems.

Sign in / Sign up

Export Citation Format

Share Document