Low-Dimensional Lattice Groups for the Continuum Mechanics of Phase Transitions in Crystals

1998 ◽  
Vol 145 (1) ◽  
pp. 1-22 ◽  
Author(s):  
G. P. Parry
Keyword(s):  
Phase Transitions ◽  
Continuum Mechanics ◽  
Dimensional Lattice ◽  
Low Dimensional ◽  
The Continuum

Indexing approximants of icosahedral quasicrystals

1999 ◽  
Vol 55 (6) ◽  
pp. 975-983 ◽  
Author(s):  
M. Quiquandon ◽  
A. Katz ◽  
F. Puyraimond ◽  
D. Gratias
Keyword(s):  
Unit Cell ◽  
Dimensional Lattice ◽  
Geometrical Properties ◽  
Actual Model ◽  
Icosahedral Quasicrystals ◽  
Low Dimensional

It is well known that the crystallography of approximants is directly related to that of the parent quasicrystal, once its unit-cell vectors are identified as parallel projections of certain N-dimensional lattice nodes {\bf A}^{i}. Derived here are explicit simple relations for calculating the shear matrices {\boldvarepsilon} and the related crystallographic properties of the corresponding approximants, including diffraction indexing and the determination of the lattice in perpendicular space. Applied to low-dimensional approximants, the derivation shows that the systematic `accidental' extinction rules observed in the pentagonal phases are generic extinctions that are due to the geometrical properties of the projected 1D lattice and are independent of the actual model of the quasicrystal.

Mechanically Optimized Orientation of Intracellular Stress Fibers Under Cyclic Stretch

2000 ◽  
Author(s):  
Hiroshi Yamada ◽  
Tohru Takemasa ◽  
Takami Yamaguchi
Keyword(s):  
Endothelial Cell ◽  
Continuum Mechanics ◽  
Cellular Response ◽  
Length Change ◽  
Mechanical Stimulus ◽  
Stress Fiber ◽  
Cyclic Stretch ◽  
Stress Fibers ◽  
Biological Phenomenon ◽  
The Continuum

Abstract To elucidate the orientation of stress fibers in a cultured endothelial cell under cyclic stretch, we hypothesized that a stress fiber aligns so as to minimize the summation of its length change under cyclic stretch, and that there is a limit in the sensitivity of cellular response to the mechanical stimulus. Results from numerical simulations based on the continuum mechanics describe the experimental observations under uniaxial stretch well. They give us an insight to the biological phenomenon of the orientation in stress fibers under biaxial stretch from the viewpoint of mechanical engineering.

Low-dimensional lattices. VI. Voronoi reduction of three-dimensional lattices

1992 ◽  
Vol 436 (1896) ◽  
pp. 55-68 ◽  
Keyword(s):  
Simple Formula ◽  
Three Dimensional ◽  
Voronoi Cell ◽  
Dimensional Lattice ◽  
Usual Treatment ◽  
Low Dimensional

The aim of this paper is to describe how the Voronoi cell of a lattice changes as that lattice is continuously varied. The usual treatment is simplified by the introduction of new parameters called the vonorms and conorms of the lattice. The present paper deals with dimensions n ≼ 3; a sequel will treat four-dimensional lattices. An elegant algorithm is given for the Voronoi reduction of a three-dimensional lattice, leading to a new proof of Voronoi’s theorem that every lattice of dimension n ≼ 3 is of the first kind, and of Fedorov’s classification of the three-dimensional lattices into five types. There is a very simple formula for the determinant of a three-dimensional lattice in terms of its conorms.

An Attempt to Provide a Unified Treatment of Tribology Through Load Carrying Capacity, Transport, and Continuum Mechanics

1980 ◽  
Vol 102 (2) ◽  
pp. 153-164 ◽  
Author(s):  
M. Godet ◽  
D. Play ◽  
D. Berthe
Keyword(s):  
High Temperature ◽  
Continuum Mechanics ◽  
Carrying Capacity ◽  
Load Carrying Capacity ◽  
Third Body ◽  
Continuum Approach ◽  
Load Carrying ◽  
Solid Liquid ◽  
Film Lubrication ◽  
The Continuum

This paper attempts to give a unified treatment of experiments obtained with solid, liquid and boundary lubricants, different plastics, high temperature steels and elastomers. The argument is centered around third body role, load-carrying capacity, transport and continuum mechanics. This study suggests that an extension to general tribology of the continuum approach used in full film lubrication could be profitable.

Analysis of Free Nonlinear Vibration Behavior for Curved Embedded Carbon Nanotubes on Elastic Foundation

2010 ◽  
Author(s):  
M. Rezaee ◽  
H. Fekrmandi
Keyword(s):  
Carbon Nanotubes ◽  
Dynamic Behavior ◽  
Continuum Mechanics ◽  
Nonlinear Term ◽  
Nonlinear Oscillations ◽  
Equation Of Motion ◽  
System Response ◽  
Response Curves ◽  
Vibration Behavior ◽  
The Continuum

Carbon nanotubes (CNTs) are expected to have significant impact on several emerging nanoelectromechanical (NEMS) applications. Vigorous understanding of the dynamic behavior of CNTs is essential for designing novel nanodevices. Recent literature show an increased utilization of models based on elastic continuum mechanics theories for studying the vibration behavior of CNTs. The importance of the continuum models stems from two points; (i) continuum simulations consume much less computational effort than the molecular dynamics simulations, and (ii) predicting nanostructures behavior through continuum simulation is much cheaper than studying their behavior through experimental verification. In numerous recent papers, CNTs were assumed to behave as perfectly straight beams or straight cylindrical shells. However, images taken by transmission electron microscopes for CNTs show that these tiny structures are not usually straight, but rather have certain degree of curvature or waviness along the nanotubes length. The curved morphology is due to process-induced waviness during manufacturing processes, in addition to mechanical properties such as low bending stiffness and large aspect ratio. In this study the free nonlinear oscillations of wavy embedded multi-wall carbon nanotubes (MWCNTs) are investigated. The problem is formulated on the basis of the continuum mechanics theory and the waviness of the MWCNTs is modeled as a sinusoidal curve. The governing equation of motion is derived by using the Hamilton’s principle. The Galerkin approach was utilized to reduce the equation of motion to a second order nonlinear differential equation which involves a quadratic nonlinear term due to the curved geometry of the beam, and a cubic nonlinear term due to the stretching effect. The system response has been obtained using the incremental harmonic balanced method (IHBM). Using this method, the iterative relations describing the interaction between the amplitude and the frequency for the single-wall nanotube and double-wall nanotube are obtained. Also, the influence of the waviness, elastic medium and van der Waals forces on frequency-response curves is researched. Results present some useful information to analyze CNT’s nonlinear dynamic behavior.

Sign in / Sign up

Export Citation Format

Share Document