Variational arguments and Noether’s theorem on the nonlinear continuum theory of dislocations

2006 ◽  
Vol 44 (8-9) ◽  
pp. 501-512 ◽  
Author(s):  
D. Sfyris ◽  
N. Charalambakis ◽  
V.K. Kalpakides
Keyword(s):  
Continuum Theory ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Nonlinear Continuum Theory ◽  
Continuum Theory Of Dislocations ◽  
Nonlinear Continuum

On the Symmetry and Stability of Thermoelastic Solids

1978 ◽  
Vol 45 (4) ◽  
pp. 740-744 ◽  
Author(s):  
J. L. Ericksen
Keyword(s):  
Phase Transitions ◽  
Continuum Theory ◽  
Nonlinear Continuum Theory ◽  
Nonlinear Continuum ◽  
Local Nature

For the most part, nonlinear continuum theory has been based on the premise that the symmetry of a material never really changes. To analyze common phase transitions, we need to revise such theory of symmetry, but this is easier said than done. What seems to be needed is a theory of symmetry which is, in some sense, more local. Classical linear theories have a local nature, dealing only with the neighborhood of some state, so it seems worthwhile to rethink what is involved in symmetry considerations for them. Here, and not only here, symmetry is strongly linked to stability. Our purpose is to elaborate these matters.

Static and Dynamic Analysis of Carbon Nanotube-Based Switches

2004 ◽  
Vol 126 (3) ◽  
pp. 230-237 ◽  
Author(s):  
Marc Dequesnes ◽  
Zhi Tang ◽  
N. R. Aluru
Keyword(s):  
Molecular Dynamics ◽  
Carbon Nanotube ◽  
Ground Plane ◽  
Continuum Theory ◽  
Continuum Approach ◽  
Nonlinear Beam ◽  
Static And Dynamic Analysis ◽  
Nonlinear Continuum Theory ◽  
Nonlinear Continuum ◽  
Beam Theories

In this paper, we report on molecular dynamics (MD), continuum (based on linear and nonlinear beam theories) and combined molecular dynamics/continuum simulation of carbon nanotube based nanoelectromechanical switches. As a prototype device, we study the pull-in voltage characteristics of a nanoelectromechanical switch made of a suspended single wall nanotube over a ground plane. The various simulations (MD, continuum and combined MD/continuum) have been performed accounting for the electrostatic and van der Waals forces between the nanotube and the ground plane. The results from the nonlinear continuum theory compared well with the results from MD, except, for cases, where nanotube buckling was observed. When buckling occurs, the electromechanical behavior of the switch is simulated by employing a combined MD/continuum approach. The combined MD/continuum approach is computationally more efficient compared to the MD simulation of the entire device. Static and dynamic pull-in, pull-in time and fundamental frequency analysis is presented for fixed-fixed and cantilever carbon nanotube switches.

Introduction

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Conservation Laws ◽  
Lagrangian Mechanics ◽  
General Introduction ◽  
Noether’S Theorem ◽  
Noether's Theorem

General introduction with a review of the principles of Hamiltonian and Lagrangian mechanics. The connection between symmetries and conservation laws, with a presentation of Noether’s theorem, is included.

scholarly journals Stochastic fractal and Noether's theorem

2021 ◽  
Vol 103 (2) ◽  
Author(s):  
Rakibur Rahman ◽  
Fahima Nowrin ◽  
M. Shahnoor Rahman ◽  
Jonathan A. D. Wattis ◽  
Md. Kamrul Hassan
Keyword(s):  
Noether’S Theorem ◽  
Noether's Theorem
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