Notes on the Nonextensive-Entropy Derived Evolution and Fundamental Metric Tensors in the Continuum Mechanics of Media and of Special and General Relativity

2017 ◽  
Author(s):  
Fredrick Zia Michael
Keyword(s):  
General Relativity ◽  
Continuum Mechanics ◽  
Nonextensive Entropy ◽  
The Continuum ◽  
Metric Tensors

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.

scholarly journals On galaxy rotation curves from a continuum mechanics approach to modified gravity

2018 ◽  
Vol 27 (02) ◽  
pp. 1850007 ◽  
Author(s):  
Christian G. Böhmer ◽  
Nicola Tamanini ◽  
Matthew Wright
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Continuum Mechanics ◽  
Modified Gravity ◽  
Galactic Rotation ◽  
Dark Matter Halos ◽  
Additional Structure ◽  
Rotation Curves ◽  
Small Deviations ◽  
Galaxy Rotation Curves

We consider a modification of General Relativity motivated by the treatment of anisotropies in Continuum Mechanics. The Newtonian limit of the theory is formulated and applied to galactic rotation curves. By assuming that the additional structure of spacetime behaves like a Newtonian gravitational potential for small deviations from isotropy, we are able to recover the Navarro–Frenk–White profile of dark matter halos by a suitable identification of constants. We consider the Burkert profile in the context of our model and also discuss rotation curves more generally.

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.

scholarly journals Theory of Nonlocal Point Transformations in General Relativity

2016 ◽  
Vol 2016 ◽  
pp. 1-32 ◽  
Author(s):  
Massimo Tessarotto ◽  
Claudio Cremaschini
Keyword(s):  
General Relativity ◽  
Field Equations ◽  
Traditional Concept ◽  
Curved Space ◽  
Point Transformations ◽  
Functional Setting ◽  
Mathematical Foundations ◽  
The Relationship ◽  
Metric Tensors

A discussion of the functional setting customarily adopted in General Relativity (GR) is proposed. This is based on the introduction of the notion of nonlocal point transformations (NLPTs). While allowing the extension of the traditional concept of GR-reference frame, NLPTs are important because they permit the explicit determination of the map between intrinsically different and generally curved space-times expressed in arbitrary coordinate systems. For this purpose in the paper the mathematical foundations of NLPT-theory are laid down and basic physical implications are considered. In particular, explicit applications of the theory are proposed, which concern(1)a solution to the so-called Einstein teleparallel problem in the framework of NLPT-theory;(2)the determination of the tensor transformation laws holding for the acceleration 4-tensor with respect to the group of NLPTs and the identification of NLPT-acceleration effects, namely, the relationship established via general NLPT between particle 4-acceleration tensors existing in different curved space-times;(3)the construction of the nonlocal transformation law connecting different diagonal metric tensors solution to the Einstein field equations; and(4)the diagonalization of nondiagonal metric tensors.

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.

A Molecular Model of Asperity Contact and Comparison to Continuum Based Models

2008 ◽  
Author(s):  
Wei Huang ◽  
Robert L. Jackson
Keyword(s):  
Contact Mechanics ◽  
Continuum Mechanics ◽  
Material Properties ◽  
Molecular Model ◽  
Small Scale ◽  
Elastic Contact ◽  
Asperity Contact ◽  
Molecular Forces ◽  
The Continuum

Surface asperities can range widely in size. Therefore it is important to characterize the effect of size and scale on the contact mechanics. This work presents a molecular model of asperity contact in order to characterize small scale asperity contact. The model is also compared to existing continuum mechanics based models developed originally by Hertz for elastic contact and later expanded by others to include plasticity. It appears that the predictions can be related to each other and that the continuum material properties can be related to the properties describing the molecular forces.

The Continuum Mechanics of Soliton Collisions

2019 ◽  
Author(s):  
Oliver Melchert ◽  
Stephanie Willms ◽  
Ihar Babushkin ◽  
Bernhard Roth ◽  
Gunter Steinmeyer ◽  
...  
Keyword(s):  
Continuum Mechanics ◽  
Soliton Collisions ◽  
The Continuum
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