3,888 research outputs found
A consistency study of coarse-grained dynamical chains through a Nonlinear wave equation of mixed type
A dynamical atomistic chain to simulate mechanical properties of a
one-dimensional material with zero temperature may be modelled by the molecular
dynamics (MD) model. Because the number of particles (atoms) is huge for a MD
model, in practice one often takes a much smaller number of particles to
formulate a coarse-grained approximation. We shall mainly consider the
consistency of the coarse-grained model with respect to the grain (mesh) size
to provide a justification to the goodness of such an approximation. In order
to reduce the characteristic oscillations with very different frequencies in
such a model, we either add a viscous term to the coarse-grained MD model or
apply a space average to the coarse-grained MD solutions for the consistency
study. The coarse-grained solution is also compared with the solution of the
(macroscopic) continuum model (a nonlinear wave equation of mixed type) to show
how well the coarse-grained model can approximate the macroscopic behavior of
the material. We also briefly study the instability of the dynamical atomistic
chain and the solution of the Riemann problem of the continuum model which may
be related to the defect of the atomistic chain under a large deformation in
certain locations.Comment: 25 pages, 15 figure
Coupling of Length Scales and Atomistic Simulation of MEMS Resonators
We present simulations of the dynamic and temperature dependent behavior of
Micro-Electro-Mechanical Systems (MEMS) by utilizing recently developed
parallel codes which enable a coupling of length scales. The novel techniques
used in this simulation accurately model the behavior of the mechanical
components of MEMS down to the atomic scale. We study the vibrational behavior
of one class of MEMS devices: micron-scale resonators made of silicon and
quartz. The algorithmic and computational avenue applied here represents a
significant departure from the usual finite element approach based on continuum
elastic theory. The approach is to use an atomistic simulation in regions of
significantly anharmonic forces and large surface area to volume ratios or
where internal friction due to defects is anticipated. Peripheral regions of
MEMS which are well-described by continuum elastic theory are simulated using
finite elements for efficiency. Thus, in central regions of the device, the
motion of millions of individual atoms is simulated, while the relatively large
peripheral regions are modeled with finite elements. The two techniques run
concurrently and mesh seamlessly, passing information back and forth. This
coupling of length scales gives a natural domain decomposition, so that the
code runs on multiprocessor workstations and supercomputers. We present novel
simulations of the vibrational behavior of micron-scale silicon and quartz
oscillators. Our results are contrasted with the predictions of continuum
elastic theory as a function of size, and the failure of the continuum
techniques is clear in the limit of small sizes. We also extract the Q value
for the resonators and study the corresponding dissipative processes.Comment: 10 pages, 10 figures, to be published in the proceedings of DTM '99;
LaTeX with spie.sty, bibtex with spiebib.bst and psfi
Chirality-dependent transmission of spin waves through domain walls
Spin-wave technology (magnonics) has the potential to further reduce the size
and energy consumption of information processing devices. In the submicrometer
regime (exchange spin waves), topological defects such as domain walls may
constitute active elements to manipulate spin waves and perform logic
operations. We predict that spin waves that pass through a domain wall in an
ultrathin perpendicular-anisotropy film experience a phase shift that depends
on the orientation of the domain wall (chirality). The effect, which is absent
in bulk materials, originates from the interfacial Dzyaloshinskii-Moriya
interaction and can be interpreted as a geometric phase. We demonstrate
analytically and by means of micromagnetic simulations that the phase shift is
strong enough to switch between constructive and destructive interference. The
two chirality states of the domain wall may serve as a memory bit or spin-wave
switch in magnonic devices.Comment: 11 pages, 10 figures (incl. supp. mat.); Phys. Rev. Lett. (accepted
Riemann solvers and undercompressive shocks of convex FPU chains
We consider FPU-type atomic chains with general convex potentials. The naive
continuum limit in the hyperbolic space-time scaling is the p-system of mass
and momentum conservation. We systematically compare Riemann solutions to the
p-system with numerical solutions to discrete Riemann problems in FPU chains,
and argue that the latter can be described by modified p-system Riemann
solvers. We allow the flux to have a turning point, and observe a third type of
elementary wave (conservative shocks) in the atomistic simulations. These waves
are heteroclinic travelling waves and correspond to non-classical,
undercompressive shocks of the p-system. We analyse such shocks for fluxes with
one or more turning points.
Depending on the convexity properties of the flux we propose FPU-Riemann
solvers. Our numerical simulations confirm that Lax-shocks are replaced by so
called dispersive shocks. For convex-concave flux we provide numerical evidence
that convex FPU chains follow the p-system in generating conservative shocks
that are supersonic. For concave-convex flux, however, the conservative shocks
of the p-system are subsonic and do not appear in FPU-Riemann solutions
Continuum-particle hybrid coupling for mass, momentum and energy transfers in unsteady fluid flow
The aim of hybrid methods in simulations is to communicate regions with
disparate time and length scales. Here, a fluid described at the atomistic
level within an inner region P is coupled to an outer region C described by
continuum fluid dynamics. The matching of both descriptions of matter is made
across an overlapping region and, in general, consists of a two-way coupling
scheme (C->P and P->C) which conveys mass, momentum and energy fluxes. The
contribution of the hybrid scheme hereby presented is two-fold: first it treats
unsteady flows and, more importantly, it handles energy exchange between both C
and P regions. The implementation of the C->P coupling is tested here using
steady and unsteady flows with different rates of mass, momentum and energy
exchange. In particular, relaxing flows described by linear hydrodynamics
(transversal and longitudinal waves) are most enlightening as they comprise the
whole set of hydrodynamic modes. Applying the hybrid coupling scheme after the
onset of an initial perturbation, the cell-averaged Fourier components of the
flow variables in the P region (velocity, density, internal energy, temperature
and pressure) evolve in excellent agreement with the hydrodynamic trends. It is
also shown that the scheme preserves the correct rate of entropy production. We
discuss some general requirements on the coarse-grained length and time scales
arising from both the characteristic microscopic and hydrodynamic scales.Comment: LaTex, 12 pages, 9 figure
- …