scholarly journals Formulation of 2D Graphene Deformation Based on Chiral-Tube Base Vectors

2010 ◽  
Vol 2010 ◽  
pp. 1-7
Author(s):  
Bohua Sun
Keyword(s):  
Molecular Dynamics ◽  
Shell Model ◽  
Continuum Model ◽  
Real Space ◽  
Honeycomb Lattice ◽  
Mechanical Behaviors ◽  
Future Studies ◽  
Physical Components ◽  
Intrinsic Feature ◽  
The Continuum

The intrinsic feature of graphene honeycomb lattice is defined by its chiral index (n,m), which can be taken into account when using molecular dynamics. However, how to introduce the index into the continuum model of graphene is still an open problem. The present manuscript adopts the continuum shell model with single director to describe the mechanical behaviors of graphene. In order to consider the intrinsic features of the graphene honeycomb lattice—chiral index (n,m), the chiral-tube vectors of graphene in real space have been used for construction of reference unit base vectors of the shell model; therefore, the formulations will contain the chiral index automatically, or in an explicit form in physical components. The results are quite useful for future studies of graphene mechanics.

scholarly journals General continuum model for twisted bilayer graphene and arbitrary smooth deformations

2019 ◽  
Vol 7 (4) ◽  
Author(s):  
Leon Balents
Keyword(s):  
Continuum Model ◽  
Bilayer Graphene ◽  
Real Space ◽  
Lattice Deformation ◽  
Displacement Fields ◽  
Simple Derivation ◽  
Twisted Bilayer Graphene ◽  
General Continuum ◽  
The Continuum

We present a simple derivation of a continuum Hamiltonian for bilayer graphene with an arbitrary smooth lattice deformation – technically in a fashion parametrized by displacement fields with small gradients. We show that this subsumes the continuum model of Bistritzer and Macdonald for twisted bilayer graphene as well as many generalizations and extensions of it. The derivation is carried out entirely in real space.

A Comparison of Coupling Molecular Dynamics to General Finite Elements

2009 ◽  
Author(s):  
Michael F. Macri
Keyword(s):  
Molecular Dynamics ◽  
Finite Element ◽  
Finite Elements ◽  
Finite Element Methods ◽  
Continuum Model ◽  
Partition Of Unity ◽  
Multiscale Model ◽  
Moving Least Squares ◽  
Interpolation Functions ◽  
The Continuum

In this paper, we assess the ability of three interpolation functions in a discretized continuum model to capture and accurately represent the solution. In particular we examine the differences between the partition of unity, moving least squares and finite element methods in the continuum part of the multiscale model.

Real-Space X-Ray Pair Distribution Function Analysis and Molecular-Dynamics Modelling of Diflunisal Channel Hydrates

2020 ◽  
Author(s):  
Anuradha Pallipurath ◽  
Francesco Civati ◽  
Jonathan Skelton ◽  
Dean Keeble ◽  
Clare Crowley ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Distribution Function ◽  
Structural Dynamics ◽  
First Principles ◽  
Pair Distribution Function ◽  
Function Analysis ◽  
Real Space ◽  
X Ray ◽  
Dynamics Modelling ◽  
Dynamics Simulations

X-ray pair distribution function analysis is used with first-principles molecular dynamics simulations to study the co-operative H<sub>2</sub>O binding, structural dynamics and host-guest interactions in the channel hydrate of diflunisal.

scholarly journals Hierarchical modeling of mechano-chemical dynamics of epithelial sheets across cells and tissue

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yoshifumi Asakura ◽  
Yohei Kondo ◽  
Kazuhiro Aoki ◽  
Honda Naoki
Keyword(s):  
Wound Healing ◽  
Cell Migration ◽  
Continuum Model ◽  
Tissue Level ◽  
Chemical Signals ◽  
Cellular Level ◽  
Mathematical Framework ◽  
Collective Cell Migration ◽  
The Continuum ◽  
Cell Cell

AbstractCollective cell migration is a fundamental process in embryonic development and tissue homeostasis. This is a macroscopic population-level phenomenon that emerges across hierarchy from microscopic cell-cell interactions; however, the underlying mechanism remains unclear. Here, we addressed this issue by focusing on epithelial collective cell migration, driven by the mechanical force regulated by chemical signals of traveling ERK activation waves, observed in wound healing. We propose a hierarchical mathematical framework for understanding how cells are orchestrated through mechanochemical cell-cell interaction. In this framework, we mathematically transformed a particle-based model at the cellular level into a continuum model at the tissue level. The continuum model described relationships between cell migration and mechanochemical variables, namely, ERK activity gradients, cell density, and velocity field, which could be compared with live-cell imaging data. Through numerical simulations, the continuum model recapitulated the ERK wave-induced collective cell migration in wound healing. We also numerically confirmed a consistency between these two models. Thus, our hierarchical approach offers a new theoretical platform to reveal a causality between macroscopic tissue-level and microscopic cellular-level phenomena. Furthermore, our model is also capable of deriving a theoretical insight on both of mechanical and chemical signals, in the causality of tissue and cellular dynamics.

Advances in the study of the mechanochemical coupling of kinesin

2018 ◽  
Vol 32 (18) ◽  
pp. 1840001 ◽  
Author(s):  
Ming Li ◽  
Zhong-Can Ou-Yang ◽  
Yao-Gen Shu
Keyword(s):  
Molecular Dynamics ◽  
Single Molecule ◽  
Intracellular Transport ◽  
Coordination Mechanism ◽  
Personal Perspective ◽  
Long Distance ◽  
Future Studies ◽  
Mechanochemical Coupling ◽  
Dynamics Simulations ◽  
Made In

Kinesin is a two-headed linear motor for intracellular transport. It can walk a long distance in a hand-over-hand manner along the track before detaching (i.e., high processivity), and it consumes one ATP molecule for each step (i.e., tight mechanochemical coupling). The mechanisms of the coordination of its two heads and the mechanochemical coupling are the central issues of numerous researches. A few advances have been made in recent decades, thanks to the development of single-molecule technologies and molecular dynamics simulations. In this paper, we review some progress of the studies on the kinematics, energetics, coordination mechanism, mechanochemical mechanism of kinesin. We also present a personal perspective on the future studies of kinesin.

The continuum shell-model neutron states of209Pb

Pramana ◽  
2003 ◽  
Vol 61 (6) ◽  
pp. 1079-1088
Author(s):  
Ramendra Nath Majumdar
Keyword(s):  
Shell Model ◽  
The Continuum

THE ATOMIC FINITE ELEMENT METHOD AS A BRIDGE BETWEEN MOLECULAR DYNAMICS AND CONTINUUM MECHANICS

2011 ◽  
Vol 03 (01n02) ◽  
pp. 39-47 ◽  
Author(s):  
R. NEUGEBAUER ◽  
R. WERTHEIM ◽  
U. SEMMLER
Keyword(s):  
Finite Element Method ◽  
Molecular Dynamics ◽  
Finite Element ◽  
High Performance ◽  
Cutting Tools ◽  
Deposition Process ◽  
Dislocation Behavior ◽  
Crystal Plasticity Fem ◽  
The Continuum ◽  
Element Method

On cutting tools for high performance cutting (HPC) processes or for hard-to-cut materials, there is an increased importance in so-called superlattice coatings with hundreds of layers each of which is only a few nanometers in thickness. Homogeneity or average material properties based on the properties of single layers are not valid in these dimensions any more. Consequently, continuum mechanical material models cannot be used for modeling the behavior of nanolayers. Therefore, the interaction potentials between the single atoms should be considered. A new, so-called atomic finite element method (AFEM) is presented. In the AFEM the interatomic bonds are modeled as nonlinear spring elements. The AFEM is the connection between the molecular dynamics (MD) method and the crystal plasticity FEM (CPFEM). The MD simulates the atomic deposition process. The CPFEM considers the behavior of anisotropic crystals using the continuum mechanical FEM. On one side, the atomic structure data simulated by MD defines the interface to AFEM. On the other side, the boundary conditions (displacements and tractions) of the AFEM model are interpolated from the CPFEM simulations. In AFEM, the lattice deformation, the crack and dislocation behavior can be simulated and calculated at the nanometer scale.

Metallic solutions of the continuum model for conducting polymers

1994 ◽  
Vol 506 (2) ◽  
pp. 92-106
Author(s):  
H. W. Streitwolf ◽  
H. Puff
Keyword(s):  
Conducting Polymers ◽  
Continuum Model ◽  
The Continuum
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