Theoretical Study of Surface Interaction Stresses Considering One-Dimensional Material Distributions in the In-Plane Direction Based on the Lennard-Jones Potential

2016 ◽  
Author(s):  
Hiroshige Matsuoka ◽  
Teppei Tanaka ◽  
Ryoya Miyake ◽  
Shigehisa Fukui
Keyword(s):  
Half Space ◽  
Material Distribution ◽  
Elementary Functions ◽  
Jones Potential ◽  
One Dimensional ◽  
Single Interface ◽  
Periodic Distribution ◽  
Lennard Jones ◽  
Plane Direction ◽  
Basic Characteristics

The interaction stresses acting between a half-space consisting of a uniform material and a half-space with a one-dimensional material distribution in the in-plane direction have been derived. Two patterns of the material distribution are considered: a periodic distribution of materials (Pattern 1) and a distribution of two materials with a single interface (Pattern 2). The interaction stresses for Pattern 1 were derived using a Fourier series, while the interaction stresses for Pattern 2 were derived as elementary functions. The basic characteristics of these interaction stresses were clarified.

Theoretical Study of van der Waals Dispersion Pressures Considering One-Dimensional Material Distributions in In-Plane Direction

2013 ◽  
Author(s):  
Hiroshige Matsuoka ◽  
Niki Kitahama ◽  
Teppei Tanaka ◽  
Shigehisa Fukui
Keyword(s):  
Half Space ◽  
Theoretical Study ◽  
Van Der Waals ◽  
Material Distribution ◽  
Elementary Functions ◽  
One Dimensional ◽  
Single Interface ◽  
Periodic Distribution ◽  
Plane Direction ◽  
Basic Characteristics

The van der Waals (vdW) dispersion pressures between a half-space consisting of a uniform material and a half-space with one-dimensional material distribution in the in-plane direction have been theoretically derived. Two patterns of material distribution were considered here, i.e., a periodic distribution of materials (Pattern 1) and a distribution of two materials with single interface (Pattern 2). The vdW pressure for Pattern 1 was derived based on a Fourier series, while the vdW pressure for Pattern 2 was derived as elementary functions. The basic characteristics of these vdW pressures were clarified.

Theoretical Analyses of Surface Interaction Stresses Considering Two-Dimensional Periodic Material Distributions

2017 ◽  
Author(s):  
Hiroshige Matsuoka ◽  
Ryoya Miyake ◽  
Satoru Maegawa ◽  
Shigehisa Fukui
Keyword(s):  
Half Space ◽  
Shear Stresses ◽  
Material Distribution ◽  
Two Dimensional ◽  
Jones Potential ◽  
Lennard Jones ◽  
Complex Fourier Series ◽  
Spatially Periodic ◽  
Basic Characteristics ◽  
Theoretical Analyses

The interaction stresses (pressure and shear stress) for (001) surface between a half-space consisting of a uniform material and a half-space with a spatially periodic material distribution have been derived based on the Lennard-Jones potential. The periodically distributed material property function is expanded as a complex Fourier series. The interaction pressures consist of non-fluctuation terms and fluctuation terms, while the shear stresses have only fluctuation terms. The interaction stresses for a distribution of two materials were then calculated as a typical example of a periodic material distribution. The basic characteristics of the interaction stresses are clarified.

Stress Distributions in an Elastic Body due to Molecular Interactions Considering One-Dimensional Periodic Material Distribution Based on Mindlin Solution

2018 ◽  
Author(s):  
Hiroshige Matsuoka ◽  
Toshiki Otani ◽  
Shigehisa Fukui
Keyword(s):  
Stress Distribution ◽  
Elastic Body ◽  
Molecular Interactions ◽  
Material Distribution ◽  
Stress Distributions ◽  
One Dimensional ◽  
Calculation Results ◽  
Basic Characteristics ◽  
The One

A method to calculate the stress distributions in the elastic body caused by the molecular interactions has been established. The stress distribution was calculated based on the Mindlin’s solution considering the one-dimensional periodic material distribution. The calculation results for a distribution of two materials were presented. The basic characteristics of the stress distribution in the elastic body were quantitatively clarified.

Cluster Dynamics for Multiscale Interactions

2003 ◽  
Author(s):  
D. Y. Tzou ◽  
J. K. Chen ◽  
R. Roybal ◽  
J. E. Beraun
Keyword(s):  
Heat Transport ◽  
Dynamics Simulation ◽  
Cluster Approach ◽  
Jones Potential ◽  
One Dimensional ◽  
Multi Scale ◽  
Lennard Jones ◽  
Geometrical Shapes ◽  
Different Shapes ◽  
Molecular Clustering

A cluster approach has been proposed to describe the process of heat transport in microscale. Molecular clustering is described by integrating the Lennard-Jones potential over specific physical domains, forming cluster potentials that possess repulsive and attractive forces sensitively varying with the geometrical shapes of the molecular clusters. The cluster potentials thus developed provides a consistent approach for describing multi-scale heat transport, in that different shapes/dimensions of the clusters take different exponents in the repulsive and attractive forces. A one-dimensional example is given to illustrate the essence of the cluster dynamics simulation, emphasizing devious behavior from molecular motion and replacement of physical boundaries by cluster potentials of a larger scale.

Sign in / Sign up

Export Citation Format

Share Document