Nanomechanics Research Papers - Academia.edu (original) (raw)

In order to prevent the spurious wave reflections and to improve the computational
efficiency in nanomechanical simulation, this dissertation performs a series of
theoretical/numerical studies on the crystalline solid material, including nanomechanics of
monatomic lattice, isothermally non-reflecting boundary condition, fast updating of neighbor
list, and the application/simulation in laser-assisted nano-imprinting.
Firstly, the nanomechanical and statistical behavior of monatomic crystal lattice are
introduced, which is the foundation for the development of non-reflecting boundary condition
and the simulation of corresponding nano materials. Based on the assumptions and the
harmonic approximation for the utilized inter-atomic potential, the equation of motion as well
as dispersive relation will be given. Furthermore, from the statistical properties of phonon
and lattice energy, the thermal amplitude can be calculated and lattice temperature can be
defined, which covers the result previously derived by other researchers at high temperatures.
Method of Time-History-Kernel (THK) and method of absorbing boundary layer (ABL)
are two main philosophies to derive the generalized Langevin equation, which is a general
form of non-reflecting boundary conditions. The general concepts of THK method, including
the formulation, kernel generation, time convolution, application assessments and numerical
verification, are given. Based on the Crump’s method to express the THK function in the
exponential form, a recursive algorithm for THK time-convolution has been proposed to reduce the computational cost from O(N 2 ) down to O(N). By applying the THK method
in lattice relaxation and the system under external forcing or heating, it is demonstrated that
the THK method indeed provides an isothermally non-reflecting boundary condition in
nanomechanical computation.
In ABL methods, two major mapping formulations are proposed and the corresponding
performances are discussed analytically as well as verified numerically. Starting from the
ω -mapping formulation, a series of extensive ABL methods are developed and investigated
to improve the performance of wave absorption, and one ABL method is recommended due
to its lower reflection at low frequency. Finally, the general comparison for all non-reflecting
boundary condition is addressed.
Based on a rigorous definition of Verlet radius with respect to temperature and
list-updating interval, this study gives an estimation formula of computation time, with which
the best algorithm can be chosen according to different total number of atoms, system
average density and system average temperature in the nanomechanical system. It has been
shown that the Verlet Cell-linked List (VCL) algorithm is better than other algorithms for a
system with a large number of atoms. Furthermore, a generalized VCL (GVCL) algorithm
optimized with a list-updating interval and cell-dividing number is analyzed and shows the
reduction of the computation time by 30% ~ 60%, which is verified by the
molecular-dynamics simulation for a two-dimensional system.
Finally, the molecular dynamics simulation accompanied with the isothermally
non-reflecting boundary condition is performed to analyze the related material physics in
laser-assisted nano-imprinting. Results show that the implemented boundary condition relax
the lattice well, and eventually absorb the wave propagation of momentum/energy during
heating and imprinting process. Besides, the temperature/force evolution in substrate, effect
of the molding-demolding interval, and surface situation of mold are discussed